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

0,4

Links

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

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

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 *)

Prog

(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

Crossrefs

Cf. A000045, A007552, A256180.

Sequence in context: A298066 A298715 A380084 * A071699 A096639 A092773

Adjacent sequences: A006698 A006699 A006700 * A006702 A006703 A006704

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved