A203694 v(n+1)/v(n), where v=A203693.

7, 837, 546364, 1193379075, 6644086647237, 79301495255509072, 1800387492184752516864, 71233673448265142887288125, 4594697931876986561881103171875, 458419756376283291989575799311713024

Offset

1,1

Comments

See A093883 for a discussion and guide to related sequences.

Links

Table of n, a(n) for n=1..10.

Formula

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

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}]          (* A203693 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203694 *)
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 *)

Crossrefs

Sequence in context: A279120 A047788 A251698 * A269896 A087350 A308296

Adjacent sequences: A203691 A203692 A203693 * A203695 A203696 A203697

Keyword

nonn

Author

Clark Kimberling, Jan 04 2012

Status

approved