A203678 v(n+1)/v(n), where v=A203677.

17, 7954, 23557648, 249581834276, 6985971879768576, 428313101742584476552, 50648802606721926260916224, 10537561069087080809570265074448, 3598422455223499123258044906373120000, 1910287477970606754101128649923632473220896

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^2; z = 12;
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}]          (* A203677 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203678 *)
Table[Product[k^4 + (n + 1)^4, {k, 1, n}], {n, 1, 12}] (* Vaclav Kotesovec, Sep 08 2023 *)

Formula

a(n) ~ 2^(n + 1/2) * (1 + sqrt(2))^(sqrt(2)*(n+1)) * exp((n+1)*Pi/sqrt(2) - 4*n) * n^(4*n). - Vaclav Kotesovec, Sep 08 2023