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%I #14 Jul 22 2018 11:14:49
%S 1,1,2,6,18,90,420,2220,19020,130860,1096920,9862920,83843640,
%T 1411202520,16144792560,203091829200,2989264122000,37012939750800,
%U 597962683188000,8681244913692000,126467701221607200,5006833609034743200,95602098255580238400
%N Number of permutations of [n] whose cycle lengths are Fibonacci numbers.
%H Alois P. Heinz, <a href="/A273001/b273001.txt">Table of n, a(n) for n = 0..451</a>
%F E.g.f.: exp(Sum_{n>=2} x^F(n)/F(n)) with F = A000045.
%p a:= proc(n) option remember; `if`(n=0, 1, add(
%p `if`(issqr(5*j^2+4) or issqr(5*j^2-4),
%p a(n-j)*(j-1)!*binomial(n-1, j-1), 0), j=1..n))
%p end:
%p seq(a(n), n=0..25);
%t a[n_] := a[n] = If[n == 0, 1, Sum[If[IntegerQ @ Sqrt[5*j^2+4] || IntegerQ @ Sqrt[5*j^2-4], a[n-j]*(j-1)!*Binomial[n-1, j-1], 0], {j, 1, n}]]; Table[ a[n], {n, 0, 25}] (* _Jean-François Alcover_, Jan 30 2017, translated from Maple *)
%Y Cf. A000045, A193374, A205801, A218002, A272603, A273994, A317128.
%K nonn
%O 0,3
%A _Alois P. Heinz_, May 12 2016
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