A203519 - OEIS

%I #12 Apr 09 2021 03:43:56

%S 3,20,336,12870,1270080,311323584,197399802600,321880885724160,

%T 1365311591573529600,15068868587132753685600,

%U 434169705562891299584593920,32678748925653999616045678080000,6431834564578466234122576826339121600

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

%F 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

%t f[j_] := Fibonacci[j + 1]; z = 15;

%t v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]

%t d[n_] := Product[(i - 1)!, {i, 1, n}] (* A000178(n-1) *)

%t Table[v[n], {n, 1, z}]                (* A203518 *)

%t Table[v[n + 1]/v[n], {n, 1, z - 1}]   (* A203519 *)

%t Table[v[n]/d[n], {n, 1, 20}]          (* A203520 *)

%Y Cf. A203518, A000045, A093883.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 03 2012