A246614 Number of endofunctions on [n] whose cycle lengths are multiples of 7.

1, 0, 0, 0, 0, 0, 0, 720, 40320, 1632960, 60480000, 2213719200, 82771476480, 3211179491520, 130247609057280, 5542874078742000, 247828800444825600, 11643316737494682240, 574455837701776343040, 29734324379435446505280, 1612668074301849600000000

Offset: 0

Author

Alois P. Heinz, Aug 31 2014

Keywords

• nonn

Links

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

Crossrefs

Column k=7 of A246609.

Programs

Maple

with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1,
      `if`(i>n, 0, add(b(n-i*j, i+7)*(i-1)!^j*
      multinomial(n, n-i*j, i$j)/j!, j=0..n/i)))
    end:
a:= a->add(b(j, 7)*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..25);

Mathematica

CoefficientList[Series[1/(1+LambertW[-x]^7)^(1/7),{x,0,20}],x] * Range[0,20]!  (* Vaclav Kotesovec, Sep 01 2014 *)

Formula

E.g.f.: 1/(1+LambertW(-x)^7)^(1/7). - Vaclav Kotesovec, Sep 01 2014

a(n) ~ n^(n-3/7) * 2^(3/7) * (sqrt(Pi) / (7^(1/7) * Gamma(1/14))) * (1 - 10 * sqrt(2/n) * Gamma(1/14) / (49 * Gamma(4/7))). - Vaclav Kotesovec, Sep 01 2014