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a(n) = floor( Gamma(n + 1/4)/Gamma(1/4) ).
3

%I #17 Sep 08 2022 08:44:44

%S 1,0,0,0,2,9,50,318,2310,19060,176310,1807181,20330788,249052161,

%T 3299941145,47024161317,717118460090,11653174976468,201017268344078,

%U 3668565147279423,70619879085128903,1430052551473860292

%N a(n) = floor( Gamma(n + 1/4)/Gamma(1/4) ).

%H G. C. Greubel, <a href="/A020087/b020087.txt">Table of n, a(n) for n = 0..450</a>

%p Digits:= 64: x:=1/4: A020087:= proc(n,x) trunc(GAMMA(n+x)/GAMMA(x)); end;

%p seq(floor(pochhammer(1/4,n)), n = 0..25); # _G. C. Greubel_, Nov 17 2019

%t Floor[Pochhammer[1/4, Range[0, 25]]] (* _G. C. Greubel_, Nov 19 2018 *)

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

%o (Magma) [Truncate(Gamma(n + 1/4)/Gamma(1/4)): n in [0..30]]; // _G. C. Greubel_, Nov 19 2018

%o (Sage) [int(gamma(n + 1/4)/gamma(1/4)) for n in range(30)] # _G. C. Greubel_, Nov 19 2018

%Y Cf. A020042, A020087.

%K nonn

%O 0,5

%A _Simon Plouffe_