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A020073 a(n) = floor( Gamma(n+1/8)/Gamma(1/8) ).

%I A020073 #14 Sep 08 2022 08:44:44
%S A020073 1,0,0,0,0,3,19,120,861,7000,63875,646742,7195012,87239530,1145018831,
%T A020073 16173391001,244622538902,3944538439805,67550220781671,
%U A020073 1224347751667801,23415650750646695,471239971356764753
%N A020073 a(n) = floor( Gamma(n+1/8)/Gamma(1/8) ).
%H A020073 G. C. Greubel, <a href="/A020073/b020073.txt">Table of n, a(n) for n = 0..445</a>
%p A020073 Digits := 64:f := proc(n,x) trunc(GAMMA(n+x)/GAMMA(x)); end;
%p A020073 seq(floor(pochhammer(1/8,n)), n = 0..25); # _G. C. Greubel_, Nov 17 2019
%t A020073 Floor[Pochhammer[1/8, Range[0, 25]]] (* _G. C. Greubel_, Nov 17 2019 *)
%o A020073 (PARI) A020073(n)=if(n==0, 1, truncate(prod(i=1,n,n-i+1/8)) );
%o A020073 for(n=0,30, print(A020073(n), " ")) \\ _R. J. Mathar_, Feb 07 2008
%o A020073 (PARI) vector(26, n, my(x=1/8); gamma(n-1+x)\gamma(x) ) \\ _G. C. Greubel_, Nov 17 2019
%o A020073 (Magma) [Floor(Gamma(n+1/8)/Gamma(1/8)): n in [0..25]]; // _G. C. Greubel_, Nov 17 2019
%o A020073 (Sage) [floor(rising_factorial(1/8, n)) for n in (0..25)] # _G. C. Greubel_, Nov 17 2019
%Y A020073 Cf. A020070, A020071, A020072.
%K A020073 nonn
%O A020073 0,6
%A A020073 _Simon Plouffe_