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a(n) = floor( Gamma(n + 3/5)/Gamma(3/5) ).
5

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

%S 1,0,0,2,8,41,231,1527,11610,99850,958561,10160755,117864768,

%T 1485096081,20197306708,294880677941,4600138575887,76362300359740,

%U 1343976486331425,24997962645764522,489960067856984638

%N a(n) = floor( Gamma(n + 3/5)/Gamma(3/5) ).

%H G. C. Greubel, <a href="/A020083/b020083.txt">Table of n, a(n) for n = 0..449</a>

%p Digits:= 64: x:=3/5: f:= proc(n,x) trunc(GAMMA(n+x)/GAMMA(x)); end;

%p seq(floor(pochhammer(3/5,n)), n = 0..25); # _G. C. Greubel_, Nov 17 2019

%t Floor[Pochhammer[3/5, Range[0, 25]]] (* _G. C. Greubel_, Nov 19 2018 *)

%o (PARI) vector(26, n, my(x=3/5); gamma(n-1+x)\gamma(x) ) \\ _G. C. Greubel_, Nov 19 2018

%o (Magma) [Truncate(Gamma(n + 3/5)/Gamma(3/5)): n in [0..30]]; // _G. C. Greubel_, Nov 19 2018

%o (Sage) [int(gamma(n + 3/5)/gamma(3/5)) for n in range(30)] # _G. C. Greubel_, Nov 19 2018

%Y Cf. A020038, A020128.

%Y Cf. A020082, A020084, A020085.

%K nonn

%O 0,4

%A _Simon Plouffe_