A006701 - OEIS

%I #16 Jun 08 2021 08:48:32

%S 0,1,1,5,13,60,246,1266,6679,39568,247940,1677435,12020295,91463410,

%T 733490265,6189608760,54746987035,506444804075,4887127598817,

%U 49096724251235,512474550910080,5548429401985372,62208756548406172,721256031012180537,8635815672831322186

%N Exponentiation of g.f. for Fibonacci numbers.

%H Vaclav Kotesovec, <a href="/A006701/b006701.txt">Table of n, a(n) for n = 0..500</a>

%F a(-1) = 1, a(n) = Sum_{k=0..n} binomial(n, k) * A000045(k) * a(n-k-1). - _Sean A. Irvine_, Jun 11 2017

%t 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 *)

%o (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

%Y Cf. A000045, A007552, A256180.

%K nonn

%O 0,4

%A _N. J. A. Sloane_.