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a(n) = floor( Gamma(n+5/8)/Gamma(5/8) ).
5

%I #14 Nov 24 2024 13:59:25

%S 1,0,1,2,9,44,251,1665,12700,109544,1054363,11202616,130230419,

%T 1644159040,22401666926,327624378797,5119130918712,85105551523594,

%U 1499985345603353,27937227061862467,548268081089050917

%N a(n) = floor( Gamma(n+5/8)/Gamma(5/8) ).

%H G. C. Greubel, <a href="/A020071/b020071.txt">Table of n, a(n) for n = 0..445</a>

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

%p seq(floor(pochhammer(5/8,n)), n = 0..25); # _G. C. Greubel_, Nov 17 2019

%t Floor[Pochhammer[5/8, Range[0, 25]]] (* _G. C. Greubel_, Nov 17 2019 *)

%t Table[Floor[(Gamma[n+5/8])/Gamma[5/8]],{n,0,20}] (* _Harvey P. Dale_, Nov 24 2024 *)

%o (PARI) vector(26, n, my(x=5/8); gamma(n-1+x)\gamma(x) ) \\ _G. C. Greubel_, Nov 17 2019

%o (Magma) [Floor(Gamma(n+5/8)/Gamma(5/8)): n in [0..25]]; // _G. C. Greubel_, Nov 17 2019

%o (Sage) [floor(rising_factorial(5/8, n)) for n in (0..25)] # _G. C. Greubel_, Nov 17 2019

%Y Cf. A020070, A020072, A020073.

%K nonn

%O 0,4

%A _Simon Plouffe_