A203473 a(n) = v(n+1)/v(n), where v=A203472.

7, 72, 990, 17160, 360360, 8910720, 253955520, 8204716800, 296541907200, 11861676288000, 520431047136000, 24858235898496000, 1284342188088960000, 71382386874839040000, 4247252019052922880000

Offset: 1

Author

Clark Kimberling, Jan 02 2012

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..250

Crossrefs

Cf. A093883, A203472, A203474.

Programs

Magma

[Floor(Gamma(2*n+6)/Gamma(n+6)): n in [1..16]]; // G. C. Greubel, Aug 27 2023

Mathematica

(* First program *)
f[j_]:= j+2; z=16;
v[n_]:= Product[Product[f[k] + f[j], {j,k-1}], {k,2,n}];
d[n_]:= Product[(i-1)!, {i,n}]  (* A000178 *)
Table[v[n], {n,z}]              (* A203472 *)
Table[v[n+1]/v[n], {n,z-1}]     (* this sequence *)
Table[v[n]/d[n], {n,20}]        (* A203474 *)
(* Second program *)
Table[Pochhammer[n+6,n], {n,20}] (* G. C. Greubel, Aug 27 2023 *)

SageMath

[rising_factorial(n+6, n) for n in range(1,16)] # G. C. Greubel, Aug 27 2023

Formula

a(n) ~ 2^(2*n + 11/2) * n^n / exp(n). - Vaclav Kotesovec, Apr 09 2021

a(n) = RisingFactorial(6 + n, n). - Peter Luschny, Mar 22 2022

Since v(n) = (135/4)*(2^(n+2)^2/Pi^(n/2))*(BarnesG(n+3)*BarnesG(n+7/2) )/( BarnesG(9/2)*BarnesG(n+6) ) then v(n+1)/v(n) = Gamma(2*n+6) / Gamma(n+6). - G. C. Greubel, Aug 27 2023