A256180 Exponential transform of the Fibonacci numbers.

1, 1, 2, 6, 21, 86, 404, 2121, 12264, 77272, 525941, 3839706, 29891370, 246906569, 2154904856, 19799299506, 190904273049, 1926229186162, 20288311652672, 222568337565537, 2537998989244956, 30029233006187756, 368050599579654557, 4665833729558724030

Offset: 0

Author

Alois P. Heinz, Mar 18 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A000045, A006701, A007552, A112005.

Row sums of A346415.

Programs

Maple

F:= n-> (<<0|1>, <1|1>>^n)[1, 2]:
a:= proc(n) option remember; `if`(n=0, 1,
      add(binomial(n-1, j-1) *F(j) *a(n-j), j=1..n))
    end:
seq(a(n), n=0..30);

Mathematica

Table[Sum[BellY[n, k, Fibonacci[Range[n]]], {k, 0, n}], {n, 0, 20}] (* Vladimir Reshetnikov, Nov 09 2016 *)

Formula

E.g.f: exp(1/sqrt(5)*(exp((1+sqrt(5))*x/2)-exp((1-sqrt(5))*x/2))).

E.g.f: exp(2/5*sqrt(5)*exp(x/2)*sinh(sqrt(5)*x/2)).