A020043 - OEIS

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

%S 1,1,1,3,11,51,287,1915,14684,127262,1230202,13122150,153091745,

%T 1939162101,26501882045,388694270000,6089543563341,101492392722343,

%U 1793032271428052,33469935733323642,658242069422031619

%N a(n) = round(Gamma(n+2/3)/Gamma(2/3)).

%C Gamma(n+2/3)/Gamma(2/3) = {1, 2/3, 10/9, 80/27, 880/81, 12320/243, 209440/729, 4188800/2187, 96342400/6561, ...}. - _R. J. Mathar_, Sep 04 2016

%H G. C. Greubel, <a href="/A020043/b020043.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(2/3,n)), n = 0..25); # _G. C. Greubel_, Dec 01 2019

%t Round[Pochhammer[2/3, Range[0, 25]]] (* _G. C. Greubel_, Dec 01 2019 *)

%o (PARI) x=2/3; vector(26, n, round(gamma(n-1+x)/gamma(x)) ) \\ _G. C. Greubel_, Dec 01 2019

%o (Magma) [Round(Gamma(n+2/3)/Gamma(2/3)): n in [0..25]]; // _G. C. Greubel_, Dec 01 2019

%o (Sage) [round(rising_factorial(2/3, n)) for n in (0..25)] # _G. C. Greubel_, Dec 01 2019

%Y Cf. A008544, A020088, A020133.

%K nonn

%O 0,4

%A _Simon Plouffe_