A273001 Number of permutations of [n] whose cycle lengths are Fibonacci numbers.

1, 1, 2, 6, 18, 90, 420, 2220, 19020, 130860, 1096920, 9862920, 83843640, 1411202520, 16144792560, 203091829200, 2989264122000, 37012939750800, 597962683188000, 8681244913692000, 126467701221607200, 5006833609034743200, 95602098255580238400

Offset: 0

Author

Alois P. Heinz, May 12 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..451

Crossrefs

Cf. A000045, A193374, A205801, A218002, A272603, A273994, A317128.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      `if`(issqr(5*j^2+4) or issqr(5*j^2-4),
       a(n-j)*(j-1)!*binomial(n-1, j-1), 0), j=1..n))
    end:
seq(a(n), n=0..25);

Mathematica

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 *)

Formula

E.g.f.: exp(Sum_{n>=2} x^F(n)/F(n)) with F = A000045.