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

0,3

Links

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

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)).

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 *)

Crossrefs

Cf. A000045, A006701, A007552, A112005.

Row sums of A346415.

Sequence in context: A090805 A150226 A326335 * A150227 A263852 A189243

Adjacent sequences: A256177 A256178 A256179 * A256181 A256182 A256183

Keyword

nonn

Author

Alois P. Heinz, Mar 18 2015

Status

approved