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

0,3

Links

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

Formula

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

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 *)

Crossrefs

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

Sequence in context: A360516 A144557 A327729 * A118455 A165774 A053505

Adjacent sequences: A272998 A272999 A273000 * A273002 A273003 A273004

Keyword

nonn

Author

Alois P. Heinz, May 12 2016

Status

approved