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a(n) = floor( Gamma(n + 4/5)/Gamma(4/5) ).
5

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

%S 1,0,1,4,15,73,426,2900,22624,199094,1951127,21072175,248651668,

%T 3182741351,43921830647,650043093588,10270680878693,172547438762055,

%U 3071344409964594,57741274907334370,1143277243165220533

%N a(n) = floor( Gamma(n + 4/5)/Gamma(4/5) ).

%H G. C. Greubel, <a href="/A020082/b020082.txt">Table of n, a(n) for n = 0..449</a>

%p Digits:= 64: x:=4/5: f:= proc(n,x) trunc(GAMMA(n+x)/GAMMA(x)); end;

%p seq(floor(pochhammer(4/5,n)), n = 0..25); # _G. C. Greubel_, Nov 17 2019

%t Floor[Pochhammer[4/5, Range[0, 25]]] (* _G. C. Greubel_, Nov 19 2018 *)

%o (PARI) vector(26, n, my(x=4/5); gamma(n-1+x)\gamma(x) ) \\ _G. C. Greubel_, Nov 19 2018

%o (Magma) [Truncate(Gamma(n + 4/5)/Gamma(4/5)): n in [0..30]]; // _G. C. Greubel_, Nov 19 2018

%o (Sage) [int(gamma(n + 4/5)/gamma(4/5)) for n in range(30)] # _G. C. Greubel_, Nov 19 2018

%Y Cf. A020037, A020127.

%Y Cf. A020083, A020084, A020085.

%K nonn

%O 0,4

%A _Simon Plouffe_