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A256180 Exponential transform of the Fibonacci numbers. 7
1, 1, 2, 6, 21, 86, 404, 2121, 12264, 77272, 525941, 3839706, 29891370, 246906569, 2154904856, 19799299506, 190904273049, 1926229186162, 20288311652672, 222568337565537, 2537998989244956, 30029233006187756, 368050599579654557, 4665833729558724030 (list; graph; refs; listen; history; text; internal format)
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. <<0, 1>>)[1, 1]:

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.

Sequence in context: A121726 A090805 A150226 * A150227 A263852 A189243

Adjacent sequences:  A256177 A256178 A256179 * A256181 A256182 A256183

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Mar 18 2015

STATUS

approved

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Last modified June 25 12:55 EDT 2019. Contains 324352 sequences. (Running on oeis4.)