A203676 v(n+1)/v(n), where v=A203675.

13, 4453, 9674704, 75224946901, 1545474559060224, 69549952010359093897, 6036862150681054978834432, 921916957672242760231518256521, 231086778644984585535258936647680000

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[j] f[k] + f[k]^2,
  {j, 1, k - 1}]
v[n_] := Product[u[n], {k, 2, n}]
Table[v[n], {n, 1, z}]          (* A203675 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203676 *)
Table[Product[k^4 - k^2*(n+1)^2 + (n+1)^4, {k, 1, n}], {n, 1, 12}] (* Vaclav Kotesovec, Nov 21 2023 *)

Formula

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