A203692 v(n+1)/v(n), where v=A203691.

13, 2709, 3024084, 11210422275, 105517529064567, 2124369691794486864, 81235403341710637909248, 5408406067938289043927788125, 586601588860841615474452259390625, 98362502736855752633918233259787105024

Offset: 1

Author

Clark Kimberling, Jan 04 2012

Keywords

• nonn

Comments

See A093883 for a discussion and guide to related sequences.

Programs

Mathematica

f[j_] := j (j + 1)/2; z = 11;
u[n_] := Product[f[j]^2 + f[j] f[k] + f[k]^2,
  {j, 1, k - 1}]
v[n_] := Product[u[n], {k, 2, n}]
Table[v[n], {n, 1, z}]          (* A203691 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203692 *)
Table[Product[k^2*(k + 1)^2/4 + k*(k + 1)*(n + 1)*(n + 2)/4 + (n + 1)^2*(n + 2)^2/4, {k, 1, n}], {n, 1, 10}] (* Vaclav Kotesovec, Nov 21 2023 *)

Formula

a(n) ~ 3^(3*n/2 + 7/4) * exp(sqrt(3)*Pi*(2*n+3)/4 - 4*n) * n^(4*n) / 2^(2*n). - Vaclav Kotesovec, Nov 21 2023