A020044 - OEIS

%I #16 Sep 08 2022 08:44:44

%S 1,0,0,1,3,15,80,506,3710,30920,288591,2982109,33797241,416832633,

%T 5557768440,79661347641,1221473997164,19950741953682,345812860530488,

%U 6339902443058941,122571447232472866,2492286093726948268

%N a(n) = round(Gamma(n+1/3)/Gamma(1/3)).

%C Gamma(n+1/3)/Gamma(1/3) = {1, 1/3, 4/9, 28/27, 280/81, 3640/243, 58240/729, 1106560/2187, ...}. - _R. J. Mathar_, Sep 04 2016

%H G. C. Greubel, <a href="/A020044/b020044.txt">Table of n, a(n) for n = 0..449</a>

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

%p seq(round(pochhammer(1/3,n)), n = 0..25); # _G. C. Greubel_, Dec 01 2019

%t Round[Pochhammer[1/3, Range[0, 25]]] (* _G. C. Greubel_, Dec 01 2019 *)

%o (PARI) x=1/3; vector(26, n, round(gamma(n-1+x)/gamma(x)) ) \\ _G. C. Greubel_, Dec 01 2019

%o (Magma) [Round(Gamma(n+1/3)/Gamma(1/3)): n in [0..25]]; // _G. C. Greubel_, Dec 01 2019

%o (Sage) [round(rising_factorial(1/3, n)) for n in (0..25)] # _G. C. Greubel_, Dec 01 2019

%Y Cf. A007559, A020089, A020134.

%K nonn

%O 0,5

%A _Simon Plouffe_