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a(n) = floor( Gamma(n + 5/6)/Gamma(5/6) ).
2

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

%S 1,0,1,4,16,80,467,3196,25042,221208,2175216,23564850,278850730,

%T 3578584368,49503750432,734305631412,11626505830701,195712848150140,

%U 3490212458677514,65732334638426516,1303691303662125905

%N a(n) = floor( Gamma(n + 5/6)/Gamma(5/6) ).

%H G. C. Greubel, <a href="/A020080/b020080.txt">Table of n, a(n) for n = 0..449</a>

%p Digits:= 64: x:=5/6: f:= proc(n,x) trunc(GAMMA(n+x)/GAMMA(x)); end;

%p seq(floor(pochhammer(5/6,n)), n = 0..25); # _G. C. Greubel_, Nov 17 2019

%t Floor[Pochhammer[5/6, Range[0, 25]]] (* _G. C. Greubel_, Nov 19 2018 *)

%o (PARI) vector(26, n, my(x=5/6); gamma(n-1+x)\gamma(x) ) \\ _G. C. Greubel_, Nov 19 2018

%o (Magma) [Truncate(Gamma(n + 5/6)/Gamma(5/6)): n in [0..30]]; // _G. C. Greubel_, Nov 19 2018

%o (Sage) [int(gamma(n + 5/6)/gamma(5/6)) for n in range(30)] # _G. C. Greubel_, Nov 19 2018

%Y Cf. A020035, A020125.

%K nonn

%O 0,4

%A _Simon Plouffe_