A203518 a(n) = Product_{2 <= i < j <= n+1} (F(i) + F(j)), where F = A000045 (Fibonacci numbers).
1, 3, 60, 20160, 259459200, 329533940736000, 102591687479575117824000, 20251578856869019790329341542400000, 6518596139761671764183992268499872995344384000000, 8899914870403074273776879003081000194727401271025610417766400000000
Offset: 1
Keywords
Programs
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Maple
F:= combinat[fibonacci]: a:= n-> mul(mul(F(i)+F(j), i=2..j-1), j=3..n+1): seq(a(n), n=1..12); # Alois P. Heinz, Jul 23 2017
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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 *) 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 * d^n * phi^(n^3/3 + n^2/2) / 5^(n^2/4), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio, d = 3.99077126463315610748163699882855013294148355045548571306491607634698645935... and c = 0.019290318831631524125422284... - Vaclav Kotesovec, Apr 09 2021
Extensions
Name edited by Alois P. Heinz, Jul 23 2017
Comments