  Copyright laws are changing all over the world, be sure to check the copyright laws for your country before posting these files!! Please take a look at the important information in this header. We encourage you to keep this file on your own disk, keeping an electronic path open for the next readers. Do not remove this. **Etexts Readable By Both Humans and By Computers, Since 1971** *These Etexts Prepared By Hundreds of Volunteers and Donations* Title: The first 498 Bernoulli Numbers Editor: Simon Plouffe April, 2001 [Etext #2586] Mathematical constants and numbers edited by Simon Plouffe Associate Professor LaCIM, University of Quebec at Montreal http://www.lacim.uqam.ca/pi : Plouffe's Inverter plouffe@math.uqam.ca We are now trying to release all our books one month in advance of the official release dates, leaving time for better editing. We produce about two million dollars for each hour we work. 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[2] Honor the etext refund and replacement provisions of this "Small Print!" statement. We are planning on making some changes in our donation structure in 2000, so you might want to email me, hart@pobox.com beforehand. *END THE SMALL PRINT! FOR PUBLIC DOMAIN ETEXTS*Ver.04.29.93*END* Mathematical constants and numbers edited by Simon Plouffe Associate Professor LaCIM, University of Quebec at Montreal http://www.lacim.uqam.ca/pi : Plouffe's Inverter plouffe@math.uqam.ca The first 498 Bernoulli numbers are the coefficients of the series expansion of t*exp(x*t)/(exp(t)-1) = sum( B(n,x)/n!*t^n, n=0..infinity ). Bernoulli(2) 1/6 Bernoulli(4) -1/30 Bernoulli(6) 1/42 Bernoulli(8) -1/30 Bernoulli(10) 5/66 Bernoulli(12) -691/2730 Bernoulli(14) 7/6 Bernoulli(16) -3617/510 Bernoulli(18) 43867/798 Bernoulli(20) -174611/330 Bernoulli(22) 854513/138 Bernoulli(24) -236364091/2730 Bernoulli(26) 8553103/6 Bernoulli(28) -23749461029/870 Bernoulli(30) 8615841276005/14322 Bernoulli(32) -7709321041217/510 Bernoulli(34) 2577687858367/6 Bernoulli(36) -26315271553053477373/1919190 Bernoulli(38) 2929993913841559/6 Bernoulli(40) -261082718496449122051/13530 Bernoulli(42) 1520097643918070802691/1806 Bernoulli(44) -27833269579301024235023/690 Bernoulli(46) 596451111593912163277961/282 Bernoulli(48) -5609403368997817686249127547/46410 Bernoulli(50) 495057205241079648212477525/66 Bernoulli(52) -801165718135489957347924991853/1590 Bernoulli(54) 29149963634884862421418123812691/798 Bernoulli(56) -2479392929313226753685415739663229/870 Bernoulli(58) 84483613348880041862046775994036021/354 Bernoulli(60) -1215233140483755572040304994079820246041491/56786730 Bernoulli(62) 12300585434086858541953039857403386151/6 Bernoulli(64) -106783830147866529886385444979142647942017/510 Bernoulli(66) 1472600022126335654051619428551932342241899101/64722 Bernoulli(68) -78773130858718728141909149208474606244347001/30 Bernoulli(70) 1505381347333367003803076567377857208511438160235/4686 Bernoulli(72) -5827954961669944110438277244641067365282488301844260429/140100870 Bernoulli(74) 34152417289221168014330073731472635186688307783087/6 Bernoulli(76) -24655088825935372707687196040585199904365267828865801/30 Bernoulli(78) 414846365575400828295179035549542073492199375372400483487/3318 Bernoulli(80) -4603784299479457646935574969019046849794257872751288919656867/230010 Bernoulli(82) 1677014149185145836823154509786269900207736027570253414881613/498 Bernoulli(84) -2024576195935290360231131160111731009989917391198090877281083932477/3404310 Bernoulli(86) 660714619417678653573847847426261496277830686653388931761996983/6 Bernoulli(88) -1311426488674017507995511424019311843345750275572028644296919890574047/61410 Bernoulli(90) 1179057279021082799884123351249215083775254949669647116231545215727922535/ 272118 Bernoulli(92) -1295585948207537527989427828538576749659341483719435143023316326829946247/1410 Bernoulli(94) 1220813806579744469607301679413201203958508415202696621436215105284649447/6 Bernoulli(96) -211600449597266513097597728109824233673043954389060234150638733420050668349987 259/4501770 Bernoulli(98) 67908260672905495624051117546403605607342195728504487509073961249992947058239/6 Bernoulli(100) -945980378191221252952274330694937218727028415330669361333856962043113954151972 47711/33330 Bernoulli(102) 3204019410860907078243020782116241775491817197152717450679002501086861530836678 158791/4326 Bernoulli(104) -319533631363830011287103352796174274671189606078272738327103470162849568365549 721224053/1590 Bernoulli(106) 3637390317261741440815182015159342716923129864058169003893081637828187987338620 2346572901/642 Bernoulli(108) -346934224784782878955208865932385254139976678576049114687000589137150126631972 4897592306597338057/209191710 Bernoulli(110) 7645992940484742892248134246724347500528752413412307906683593870759797606269585 779977930217515/1518 Bernoulli(112) -265087960215509971335259721468516201444315149919250989645178842768096675651487 5515366781203552600109/1671270 Bernoulli(114) 2173783231936916333331076108665299147572115667909083136080611011493360548423459 3650904188618562649/42 Bernoulli(116) -309553916571842976912513458033841416869004128064329844245504045721008957524571 968271388199595754752259/1770 Bernoulli(118) 3669631199697131115349471515855850066846063610806992043010594406764144850458064 61889371776354517095799/6 Bernoulli(120) -515074865350791090618439968578499832740951703532626752130928691671992974749229 85358811329367077682677803282070131/2328255930 Bernoulli(122) 4963366607926258191253263747599075743872279031106013977030931179315068321410043 1329033113678098037968564431/6 Bernoulli(124) -958767753342471287507749031075424446205788300132973368195535127293585933544359 44413631943610268472689094609001/30 Bernoulli(126) 5556330281949274850616324408918951380525567307126747246796782304333594286400508 981287241419934529638692081513802696639/4357878 Bernoulli(128) -267754707742548082886954405585282394779291459592551740629978686063357792734863 530145362663093519862048495908453718017/510 Bernoulli(130) 1928215175136130915645299522271596435307611010164728458783733020528548622403504 078595174411693893882739334735142562418015/8646 Bernoulli(132) -410951945846993378209020486523571938123258077870477502433469747962650070754704 863812646392801863686694106805747335370312946831/4206930 Bernoulli(134) 2645901718707177256336357372488790151512545255931686884119185548406677655916905 40727987316391252434348664694639349484190167/6 Bernoulli(136) -842902263433674051312875780603661936493366123975474357671892069122304422426282 12786558235455817749737691517685781164837036649737/4110 Bernoulli(138) 2694866548990880936043851683724113040849078494664282483862150893060478501559546 243423633375693325757795709438325907154973590288136429/274386 Bernoulli(140) -328949098643589880393069954885188400688053747693113098130746708516250480297361 8096693859598125274741604181467826651144393874696601946049/679470 Bernoulli(142) 1473185328088858956587008044245321423980421702399064267619487899740754606158164 3106569966189211748270209483494554402556608073385149191/6 Bernoulli(144) -305024469837360756503515583690172635740500710425656676188419185243485103374476 1276392695669329626855965183503295793517411526056244431024612640493/2381714790 Bernoulli(146) 4120570026280114871526113315907864026165545608808541153973817680034790262683524 284855810008621905238290240143481403022987037271683989824863/6 Bernoulli(148) -169173714561401897986556109511216618960768285214730140081648067591695787117864 8433284821493606361235973346584667336181793937950344828557898347149/4470 Bernoulli(150) 4633655793891627414432844258118062649822337254252957998522998073253793155015723 05760030594769688296308375193913787703707693010224101613904227979066275/2162622 Bernoulli(152) -373701814115510850210589288849128216583748953148893295176850712718240973132847 2084456653639812530140212355374618917309552824925858430886313795805601/30 Bernoulli(154) 1025971868203802105102779423837918446102573865246056923399277648975088133750686 3808448685054322627708245455888249006715516690124228801409697850408284121/138 Bernoulli(156) -817180860832626285107564597536734523135957103961164675821520905960925486991383 4694299550948828465080397683633716467049473386655982976884836350662433481896141 9869/1794590070 Bernoulli(158) 1716726769011532100721830835061033951375139222740295641505001352653081481973585 51999205867870374013289728260984269623579880772408522396975250682773558018919/6 Bernoulli(160) -424086079420331037606556349236115694998939808708637321471062577845844194047783 9981850928830420029285687066701804645453159767402961229305942765784122421197736 180867/230010 Bernoulli(162) 1584451495144416428390934243279426140836596476080786316960222380784239380974799 8803643636479781686345904182158544197937165493888659053485343756299287320087862 33507729/130074 Bernoulli(164) -205380646091432162655719795866926468378053310231486450681333723839303449483166 0059120392638854094081483317332279380432508494509482852486062609201354728133535 6200073083/2490 Bernoulli(166) 5734032969370860921631095311392645731505222358555208498573088911303001784652122 9647032057527091941930952463086112641216788342507044680826483137881247541686718 15815821441/1002 Bernoulli(168) -138448285151763960812383465850635172285311091569843452492604539343177727548367 9125898751654032498361156975864952598334740858904573417658927014305850902639224 6407576578281097477/3404310 Bernoulli(170) 1953342076266375304149767792384622344814103373509884272151399957073469791246869 1826768817153635265057253533036981817697995193147742759487278301874989469915791 7782460035894085/66 Bernoulli(172) -114437022113333284471871799429918466130080465060324217317552581486652878322649 3102478136596263330170177308847084162180432820100802012999695554946757321765958 7609679405537739509973/5190 Bernoulli(174) 4166161554662042831884959593250717297395614318182561412048180684077407803317591 2708311946192938321074824269456551433579098072518528592794831763734356976076398 83085093246499347128331/2478 Bernoulli(176) -136934791048670570764562136251282433222036077447659434835693871536660804458861 4657557436131706543948464159947970464346070253278291989696390096800799614617317 655510118710460076077638883999/1043970 Bernoulli(178) 1124251816617941290026484851206299982774720467712867275292043701618829826708395 7454596541707183631821434183145140854266928570184286149354127360639468530330943 28968069656979232446257101741/1074 Bernoulli(180) -617313645401624892464052227226347096019955932829065533753020205585339779174734 1312347030141906500993752700612233695954532816018207721731818225290076670213481 102834647254685911917265818955932383093313/7225713885390 Bernoulli(182) 4277269279349192541137304400628629348327468135828402291661683018622451659989595 5107129158104362387211395469635586552603843289887732196880914435296265313356879 51612545946030357929306651006711/6 Bernoulli(184) -857321333523056180131194437347933216431403305730705359015465649285681432317514 0106860290793244796596346423848090617113194810200307159890091405951705569561967 62318625529645723516532076273012244047/1410 Bernoulli(186) 2225864609843696805063960222181638518159656791851533816994667050059961222574248 7595012775838387331550474751212260636163500086787417640903770807353228157478339 547041472679880890292167353534100797481/42 Bernoulli(188) -141582777506237587933093868704013973331128236327174780514265220297120012607479 2078947371156216503110166561822565432921047360528161969691806131624063485798401 9071572591940586875558943580878119388321001/30 Bernoulli(190) 5411555842544259796131885546196787277987837486638756184149141588783989774511509 6087334290675173837507062994868227021716725222031067309935812427778258642034872 38429479957280273093904025319950569633979493395/12606 Bernoulli(192) -346465752997582699690191405750952366871923192340955593486485715370392154894102 0004069801625217284925019175980127114021635301665169911151221313985420290562869 59857727373568402417020319761912636411646719477318166587/868841610 Bernoulli(194) 2269186825161532962833665086968359967389321429297588337232986752409765414223476 6968631997599816118176607357538313239004564952539618371759243121088729150895349 70310604331636484174526399721365966337809334021247/6 Bernoulli(196) -627531351104611936725531066998937136031530541533118953055906391070178246402413 7848048462555457857614211583578896086553453221456098292554979868376270523131661 1716668749347221458005671217067357943416524984438771831113/171390 Bernoulli(198) 8852791486134800496840058101053056522054452640033954842943984390872119634957949 4069282285662653465989920237253162555666526385826449862863083834096823053048072 002986184254693991336699593468906111158296442729034119206322233/244713882 Bernoulli(200) -498384049428333414764928632140399662108495887457206674968055822617263669621523 6875688658023022109991326014126976132793910586545271453405158400992904780263503 82802884371712359337984274122861159800280019110197888555893671151/1366530 Bernoulli(202) 2250525326187264545900714460628885135841050444551247116222631411681549780530233 5160699575343945749225792906081804275203182356211236861094743438878579446118424 38698399885295153935574958275021715116120056995036417537079471/6 Bernoulli(204) -110636644250856903590976481422794879200517231299540994715372334521128669716264 1963338110257097477461932107868201143690258498973457225310980427605309226568788 91556664782168465095563132092311332073097630676251482491663634626858373/281190 Bernoulli(206) 2525292668891404920279427026668969389456388249389889339455604316691573384284678 2936201000669243616936664447223387438391982213479316519168076511988009359424930 38194104759967208073711284671045255047521429204396148980705984836743/6 Bernoulli(208) -124073906684330234127114734836969907263347958964127614725878540721428004033735 7708702129854106109463337735432696662327884942363192480804439782265113590564081 2063181221280972334965193338438214107578486417026806166184210160001817890901/ 27030 Bernoulli(210) 4708181368529492614110644197951837317202610608341257204206693195241245204360822 8759106130104335721332278317410972616188332065375191988858122543472191504820055 4342299722544020404147351818763644224133262180471896777520393840396571039563276 2155/9225988926 Bernoulli(212) -185611066994738826838936104068976402746416046043667192325313117685322408774192 4378432403442710398247642246902212818749685974336641529240178398124235555437625 2514810445260249103561318190166700479496616365399646623703756226308633271686963 07/3210 Bernoulli(214) 4005748930070152861935826766476856180706477227448622268042052745245798242539770 5463397898995461603415900691094670235170855786189860559691872027318782716854324 6070884111850631094386559256879136029424445176574691180899448206378373069370360 7/6 Bernoulli(216) -119931227701086178585364433229648780036181560695597948031178092796080391208188 2908800010335503659286487795456356483193236341488681178605460131851720693754960 5059298307895591515771731031691422489377098686236263367916404512751010916862894 129855138281961/15270994830 Bernoulli(218) 5646413644023523531472659729552574911763686780871700375627426663366507837122353 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92373882916779852781709/1671270 Bernoulli(226) 3168221108903401670436878558215734893322849540781208738796672473984272484396317 8495969786302720313420241946898714679161868981927712674389822287105250798869562 9510619743140121735789346089722138141066738563604926458338074963177669112159201 6493432807733153743581/1362 Bernoulli(228) -190650290999788816612320192317738583356772903915141314387627187059905770444593 9156075718972624235764657102074902610737729027517674632609562387841658709266014 3290054075335219507444491098072158087702012477249322314952529816329080423713079 65561986133763291349835081839/625170 Bernoulli(230) 1262073704490981856183285609035555562401688731960526176299768957106264664974510 7532482632213152948299491122977690702642386377706799989565320538433072623252159 4641159180572947113966254365067360415424033700252584772051018080635940567599772 72469883621048184279331863155/3102 Bernoulli(232) -227778296274954464778619309384471000058456114552786104359486685207159644007658 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