A272603 Number of permutations of [n] whose cycle lengths are factorials.

1, 1, 2, 4, 10, 26, 196, 1072, 7484, 42940, 261496, 1477136, 15219832, 134828344, 1488515120, 13692017536, 130252442896, 1123580329232, 14639510308384, 173489066401600, 2528654220104096, 31472160333513376, 402634734214583872, 4645625988351336704, 25925035549644280991680

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..455

Formula

E.g.f.: exp( sum(n>=1, x^(n!) / n! ) ).

Maple

a:= proc(n) option remember; local r, f, i;
      if n=0 then 1 else r, f, i:= $0..2;
        while f<=n do r:= r +a(n-f)*(f-1)!*
          binomial(n-1, f-1); f, i:= f*i, i+1
        od; r
      fi
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Jun 04 2016

Mathematica

nmax = 4; egf = Exp[Sum[x^n!/n!, {n, 1, nmax}]] + O[x]^(nmax! + 1); CoefficientList[egf, x]*Range[0, nmax!]! (* Jean-François Alcover, Feb 19 2017 *)

Prog

(PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(sum(n=1, 10, x^(n!)/n!))))

Crossrefs

Cf. A000142, A273001 (cycle lengths are Fibonacci numbers), A272602 (e.g.f.: exp( sum(n>=1, x^(n!) / n ) ) ), A273996, A317132.

Sequence in context: A148104 A179981 A086991 * A272602 A113066 A002459

Adjacent sequences: A272600 A272601 A272602 * A272604 A272605 A272606

Keyword

nonn

Author

Joerg Arndt, May 29 2016

Status

approved