A203512 a(n) = A203511(n+1)/A203511(n).

1, 4, 63, 2288, 151200, 15909696, 2447297356, 518678754048, 145022370451200, 51747613910720000, 22956761806169786496, 12397159038346976323584, 8008689946841913447559168, 6099405371286264105062400000, 5408896545253926024119820000000

Offset: 0

Author

Clark Kimberling, Jan 03 2012

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..220

Crossrefs

Cf. A000217, A093883, A203511.

Programs

Magma

[1] cat [(&*[(n+1)*(n+2) +j*(j+1): j in [1..n]])/2^n: n in [1..30]]; // G. C. Greubel, Feb 23 2024

Mathematica

f[j_] := j (j + 1)/2; z = 15;
v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]
Table[v[n], {n, 1, z}]               (* A203511 *)
Table[v[n + 1]/v[n], {n, 1, z - 1}]  (* A203512 *)
Table[Product[(n+2)*(n+1)/2 + j*(j+1)/2, {j, 1, n}], {n, 0, 10}] (* Vaclav Kotesovec, Sep 07 2023 *)

SageMath

def A203512(n): return product((n+1)*(n+2)+j*(j+1) for j in range(1, n+1))//2^n
[A203512(n) for n in range(31)] # G. C. Greubel, Feb 23 2024

Formula

a(n) ~ 2 * n^(2*n) / exp((2 - Pi/2)*n - 3*Pi/4). - Vaclav Kotesovec, Sep 07 2023

Extensions

More terms from Alois P. Heinz, Jul 29 2017