A203519 a(n) = v(n+1)/v(n), where v=A203518.

3, 20, 336, 12870, 1270080, 311323584, 197399802600, 321880885724160, 1365311591573529600, 15068868587132753685600, 434169705562891299584593920, 32678748925653999616045678080000, 6431834564578466234122576826339121600

Offset: 1

Author

Clark Kimberling, Jan 03 2012

Keywords

• nonn

Crossrefs

Cf. A203518, A000045, A093883.

Programs

Mathematica

f[j_] := Fibonacci[j + 1]; z = 15;
v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]
d[n_] := Product[(i - 1)!, {i, 1, n}] (* A000178(n-1) *)
Table[v[n], {n, 1, z}]                (* A203518 *)
Table[v[n + 1]/v[n], {n, 1, z - 1}]   (* A203519 *)
Table[v[n]/d[n], {n, 1, 20}]          (* A203520 *)

Formula

a(n) ~ c * phi^(n*(n+2) + 5/6) / 5^(n/2 + 1/4), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio and c = 3.990771264633156107481636998828550132941483550455485713064916076346986459357... - Vaclav Kotesovec, Apr 09 2021