A020001 Nearest integer to Gamma(n + 11/12)/Gamma(11/12).

1, 1, 2, 5, 20, 99, 584, 4038, 31970, 285070, 2826941, 30860774, 367757553, 4750201727, 66106974037, 986095696055, 15695356495548, 265513114049684, 4757109960056837, 89988663411075165, 1792274212937247027, 37488402287270750315, 821620816796017277740

Offset

0,3

Comments

Gamma(n + 11/12)/Gamma(11/12) = 1, 11/12, 253/144, 8855/1728, 416185/20736, 24554915/248832, 1743398965/2985984, 144702114095/35831808, ...

Links

Shujing Lyu, Table of n, a(n) for n = 0..449

Formula

a(n) = round(Product_{k=0..n-1} (k+11/12)). - Sean A. Irvine, Apr 14 2019

Maple

Digits := 64:f := proc(n, x) round(GAMMA(n+x)/GAMMA(x)); end:
seq(f(n, 11/12), n=0..22);

Mathematica

Table[Round[Gamma[n + #]/Gamma[#]] &[11/12], {n, 0, 20}] (* Michael De Vlieger, Apr 18 2016 *)

Prog

(PARI) a(n) = round(gamma(n+11/12)/gamma(11/12)); \\ Michel Marcus, Apr 19 2016
(Magma) [Round(Gamma(n+11/12)/Gamma(11/12)): n in [1..30]]; // G. C. Greubel, Jan 19 2018

Crossrefs

Cf. A020046, A020091.

Sequence in context: A020005 A259834 A074415 * A348597 A370699 A039909

Adjacent sequences: A019998 A019999 A020000 * A020002 A020003 A020004

Keyword

nonn

Author

Simon Plouffe

Status

approved