A020001 - OEIS

%I #31 Sep 08 2022 08:44:44

%S 1,1,2,5,20,99,584,4038,31970,285070,2826941,30860774,367757553,

%T 4750201727,66106974037,986095696055,15695356495548,265513114049684,

%U 4757109960056837,89988663411075165,1792274212937247027,37488402287270750315,821620816796017277740

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

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

%H Shujing Lyu, <a href="/A020001/b020001.txt">Table of n, a(n) for n = 0..449</a>

%F a(n) = round(Product_{k=0..n-1} (k+11/12)). - _Sean A. Irvine_, Apr 14 2019

%p Digits := 64:f := proc(n,x) round(GAMMA(n+x)/GAMMA(x)); end:

%p seq(f(n,11/12), n=0..22);

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

%o (PARI) a(n) = round(gamma(n+11/12)/gamma(11/12)); \\ _Michel Marcus_, Apr 19 2016

%o (Magma) [Round(Gamma(n+11/12)/Gamma(11/12)): n in [1..30]]; // _G. C. Greubel_, Jan 19 2018

%Y Cf. A020046, A020091.

%K nonn

%O 0,3

%A _Simon Plouffe_