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%I #15 Jul 15 2021 17:37:47
%S 1,1,2,6,21,86,404,2121,12264,77272,525941,3839706,29891370,246906569,
%T 2154904856,19799299506,190904273049,1926229186162,20288311652672,
%U 222568337565537,2537998989244956,30029233006187756,368050599579654557,4665833729558724030
%N Exponential transform of the Fibonacci numbers.
%H Alois P. Heinz, <a href="/A256180/b256180.txt">Table of n, a(n) for n = 0..500</a>
%F E.g.f: exp(1/sqrt(5)*(exp((1+sqrt(5))*x/2)-exp((1-sqrt(5))*x/2))).
%F E.g.f: exp(2/5*sqrt(5)*exp(x/2)*sinh(sqrt(5)*x/2)).
%p F:= n-> (<<0|1>, <1|1>>^n)[1, 2]:
%p a:= proc(n) option remember; `if`(n=0, 1,
%p add(binomial(n-1, j-1) *F(j) *a(n-j), j=1..n))
%p end:
%p seq(a(n), n=0..30);
%t Table[Sum[BellY[n, k, Fibonacci[Range[n]]], {k, 0, n}], {n, 0, 20}] (* _Vladimir Reshetnikov_, Nov 09 2016 *)
%Y Cf. A000045, A006701, A007552, A112005.
%Y Row sums of A346415.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Mar 18 2015
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