A006701 Exponentiation of g.f. for Fibonacci numbers.

0, 1, 1, 5, 13, 60, 246, 1266, 6679, 39568, 247940, 1677435, 12020295, 91463410, 733490265, 6189608760, 54746987035, 506444804075, 4887127598817, 49096724251235, 512474550910080, 5548429401985372, 62208756548406172, 721256031012180537, 8635815672831322186

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A000045, A007552, A256180.

Programs

Mathematica

a[-1] = 1; a[n_] := a[n] = Sum[Binomial[n, k]*Fibonacci[k]*a[n - k - 1], {k, 0, n}]; Table[a[n], {n, 0, 30}] (* Vaclav Kotesovec, Jun 08 2021 *)

PARI

a(n) = if (n==-1, 1, sum(k=0, n, binomial(n,k)*fibonacci(k)*a(n-k-1))); \\ Michel Marcus, Jun 11 2017

Formula

a(-1) = 1, a(n) = Sum_{k=0..n} binomial(n, k) * A000045(k) * a(n-k-1). - Sean A. Irvine, Jun 11 2017