login
a(n) = floor( Gamma(n+5/7)/Gamma(5/7) ).
7

%I #15 Sep 08 2022 08:44:44

%S 1,0,1,3,12,58,332,2232,17225,150103,1458149,15623031,183012659,

%T 2326875239,31911431853,469553925838,7378704548888,123329776031414,

%U 2184698889699346,40885079221516335,806020133224179176

%N a(n) = floor( Gamma(n+5/7)/Gamma(5/7) ).

%H G. C. Greubel, <a href="/A020075/b020075.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(5/7,n)), n = 0..25); # _G. C. Greubel_, Nov 17 2019

%t Floor[Pochhammer[5/7, Range[0, 25]]] (* _G. C. Greubel_, Nov 17 2019 *)

%o (PARI) vector(26, n, my(x=5/7); gamma(n-1+x)\gamma(x) ) \\ _G. C. Greubel_, Nov 17 2019

%o (Magma) [Floor(Gamma(n+5/7)/Gamma(5/7)): n in [0..25]]; // _G. C. Greubel_, Nov 17 2019

%o (Sage) [floor(rising_factorial(5/7, n)) for n in (0..25)] # _G. C. Greubel_, Nov 17 2019

%Y Cf. A220606.

%Y Cf. A020074, A020076, A020077, A020078, A020079.

%K nonn

%O 0,4

%A _Simon Plouffe_