A203696 v(n+1)/v(n), where v=A203695.

10, 1665, 1497224, 4485885300, 34184139841800, 557745681594010000, 17295475176752223859200, 934164847784800073360250000, 82223581117536608232019062500000, 11191248877703366469751902789287961600

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[k]^2, {j, 1, k - 1}]
v[n_] := Product[u[n], {k, 2, n}]
Table[v[n], {n, 1, z}]          (* A203695 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203696 *)
Table[Product[k^2*(k+1)^2/4 + (n+1)^2*(n+2)^2/4, {k, 1, n}], {n, 1, 10}] (* Vaclav Kotesovec, Nov 21 2023 *)

Formula

a(n) ~ (1 + sqrt(2))^((2*n+3)/sqrt(2)) * exp(Pi*(2*n+3)/(2*sqrt(2)) - 4*n) * n^(4*n) / 2^(n-1). - Vaclav Kotesovec, Nov 21 2023