A203512 - OEIS

%I #17 Feb 23 2024 02:31:05

%S 1,4,63,2288,151200,15909696,2447297356,518678754048,145022370451200,

%T 51747613910720000,22956761806169786496,12397159038346976323584,

%U 8008689946841913447559168,6099405371286264105062400000,5408896545253926024119820000000

%N a(n) = A203511(n+1)/A203511(n).

%H G. C. Greubel, <a href="/A203512/b203512.txt">Table of n, a(n) for n = 0..220</a>

%F a(n) ~ 2 * n^(2*n) / exp((2 - Pi/2)*n - 3*Pi/4). - _Vaclav Kotesovec_, Sep 07 2023

%t f[j_] := j (j + 1)/2; z = 15;

%t v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]

%t Table[v[n], {n, 1, z}]               (* A203511 *)

%t Table[v[n + 1]/v[n], {n, 1, z - 1}]  (* A203512 *)

%t Table[Product[(n+2)*(n+1)/2 + j*(j+1)/2, {j, 1, n}], {n, 0, 10}] (* _Vaclav Kotesovec_, Sep 07 2023 *)

%o (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

%o (SageMath)

%o def A203512(n): return product((n+1)*(n+2)+j*(j+1) for j in range(1, n+1))//2^n

%o [A203512(n) for n in range(31)] # _G. C. Greubel_, Feb 23 2024

%Y Cf. A000217, A093883, A203511.

%K nonn

%O 0,2

%A _Clark Kimberling_, Jan 03 2012

%E More terms from _Alois P. Heinz_, Jul 29 2017