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

0,8

Links

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

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

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 *)

Crossrefs

Column k=7 of A246609.

Sequence in context: A055361 A092716 A246194 * A291113 A246217 A364771

Adjacent sequences: A246611 A246612 A246613 * A246615 A246616 A246617

Keyword

nonn

Author

Alois P. Heinz, Aug 31 2014

Status

approved