A246613 Number of endofunctions on [n] whose cycle lengths are multiples of 6.

1, 0, 0, 0, 0, 0, 120, 5040, 161280, 4898880, 151200000, 4870182240, 165589522560, 5970883913280, 228632817853440, 9292843409850000, 400385970127503360, 18252778818295082880, 878619947953407528960, 44562094805330883023040, 2376296054962478899200000

Offset

0,7

Links

Alois P. Heinz, Table of n, a(n) for n = 0..300

Formula

E.g.f.: 1/(1-LambertW(-x)^6)^(1/6). - Vaclav Kotesovec, Sep 01 2014

a(n) ~ n^(n-5/12) * 2^(1/4) * (sqrt(Pi) / (3^(1/6) * Gamma(1/12))) * (1 - 85 * sqrt(2/n) * Gamma(1/12) / (432 * Gamma(7/12))). - Vaclav Kotesovec, Sep 01 2014

Maple

with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1,
      `if`(i>n, 0, add(b(n-i*j, i+6)*(i-1)!^j*
      multinomial(n, n-i*j, i$j)/j!, j=0..n/i)))
    end:
a:= a->add(b(j, 6)*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..25);

Mathematica

CoefficientList[Series[1/(1-LambertW[-x]^6)^(1/6), {x, 0, 20}], x] * Range[0, 20]!  (* Vaclav Kotesovec, Sep 01 2014 *)

Crossrefs

Column k=6 of A246609.

Sequence in context: A140907 A072419 A246193 * A031145 A126245 A221435

Adjacent sequences: A246610 A246611 A246612 * A246614 A246615 A246616

Keyword

nonn

Author

Alois P. Heinz, Aug 31 2014

Status

approved