A293130 - OEIS

%I #18 Oct 02 2017 20:13:08

%S 1,4,3,9,5,8,4,5,2,5,6,3,1,4,9,3,2,7,2,1,5,1,7,0,2,0,5,4,4,9,0,0,3,3,

%T 8,4,6,4,4,5,6,5,5,7,4,3,1,2,5,5,3,1,6,3,5,3,7,2,3,2,6,0,5,7,8,9,7,2,

%U 4,7,3,0,8,6,5,8,0,9,2,2,6,8,4,2,2,1,0,0,7,8,1,2,8,6,3,0,6,9,7,8,2,4,1,5,3,0,9,5,7,5,8,6,1,1,9,1,5,7,5,5,1,6,1,1,4,7,2,8,0,7,3,9,7,6,7,3,8,9,3,6,1,1,7,2,6,7,6,7,4,2,2,4,9,6,3,5,8,0,1,0,8,0,3,9,4,0,0,8,6,1,4,1,1,4,2,5,8,1,8,7,4,3,7,1,3,6,1,6,6,8,1,0,2,8,2,0,0,1,8,5,2

%N Constant t defined by: t = Sum_{n>=1} 1 / floor( gamma(n+t)/gamma(t) ).

%H Paul D. Hanna, <a href="/A293130/b293130.txt">Table of n, a(n) for n = 1..2000</a>

%F t = Sum_{n>=1} 1 / floor( Product_{k=0..n-1} (k + t) ).

%F t = Sum_{n>=1} 1/A293131(n), where A293131(n) = floor(Product_{k=0..n-1} (k + t)).

%e This constant t is defined by

%e t = 1/[t] + 1/[t*(1+t)] + 1/[t*(1+t)*(2+t)] + 1/[t*(1+t)*(2+t)*(3+t)] + 1/[t*(1+t)*(2+t)*(3+t)*(4+t)] + 1/[t*(1+t)*(2+t)*(3+t)*(4+t)*(5+t)] + 1/[t*(1+t)*(2+t)*(3+t)*(4+t)*(5+t)*(6+t)] + 1/[t*(1+t)*(2+t)*(3+t)*(4+t)*(5+t)*(6+t)*(7+t)] +...

%e where [x] is the floor function of x.

%e Explicitly, t is the sum of the infinite series of unit fractions

%e t = 1 + 1/3 + 1/12 + 1/53 + 1/291 + 1/1878 + 1/13975 + 1/117949 + 1/1113390 + 1/11623335 + 1/132966129 + 1/1654043412 + 1/22229656253 + 1/320987000444 + 1/4955905924999 + 1/81473034355102 + 1/1420855869195491 + 1/26199991898769875 + 1/509316957086997352 + 1/10410226994717110400 + 1/223190941584248205202 + 1/5008311999035018587226 + 1/117392752432115751942460 + 1/2869030095761224977541954 + 1/72986933627698300236793754 + 1/1929744200916184847850410278 + 1/52951379113886857052967930528 + 1/1505915222058143312106047567382 + 1/44333518468215829832469997051113 + 1/1349493882731900596771978592981358 +...+ 1/A293131(n) +...

%e where A293131(n) = floor( gamma(n+t)/gamma(t) ).

%e The gamma function of t begins:

%e gamma(t) = 0.88581292008941981278905841201602316593162655110412781217...

%e The decimal expansion of the constant begins:

%e t = 1.43958452563149327215170205449003384644565574312553\

%e 16353723260578972473086580922684221007812863069782\

%e 41530957586119157551611472807397673893611726767422\

%e 49635801080394008614114258187437136166810282001852\

%e 71986524115283147181117613091464099152464344842194\

%e 03130782239819712020783909070772646562174382319601\

%e 87901109174676702574585741493758869423683283302132\

%e 19772471377032093310941373611388876361314271966189\

%e 51687129567401125902522698271243130375515730344144\

%e 89398504298317880132453598772037634155976591780521\

%e 17923774492711461792764326635007336455882638091226\

%e 30796650668192788163602841905506059461656078746236\

%e 24620578796218665453036847516136824206580370036312\

%e 73379175306639573926145224686145601578124507300305\

%e 84188067765705158712515491816705192407489451135262\

%e 86190181616703980708946025822449467960139056972077\

%e 40797366614187428360507507342927211168684236773137\

%e 49294143987080470449032331057452351336014297439184\

%e 50430557156584749123218047693367884635083738677873\

%e 34019674977793547337375843041736088849917290621639\

%e 54389852553420480346353414919523708146738903410993\

%e 01233859364772149707547341029827962425502915272879\

%e 35927631073694435379797551155875907341158582729140\

%e 48357792934899982767160212975485636211452685422411\

%e 97750583668403685526752220714544411739322089041786\

%e 47472784769383100878345814573963489580745215743161\

%e 34101260599898250324408071209287416844546576679828\

%e 79209902086793019530239468625339504507647895589209\

%e 85303626534482276737567070400346537075960151406652\

%e 91201226973295295411721705817522528694811983355579\

%e 30968457719586128867890291158799018076747738874511\

%e 91956170297985333889975995109777626582090431672462\

%e 69746949754661646216920177221895419536721000305683\

%e 43574448536273273114489138972600109548422716852883\

%e 33691388438786126807689424216476053233668428723892\

%e 17238144570510561082073268842749039044087563882981\

%e 11951204498793579405398580185429576405630930517014\

%e 81915539926643164796767912245359092601523055879266\

%e 00302904969244782163649633424417272066067277372356\

%e 12974480645261857901432928896560897591776004010828...

%Y Cf. A293131.

%K nonn,cons

%O 1,2

%A _Paul D. Hanna_, Sep 30 2017