A246612 Number of endofunctions on [n] whose cycle lengths are multiples of 5.

1, 0, 0, 0, 0, 24, 720, 17640, 430080, 11022480, 302835456, 8976567600, 287236730880, 9901354268520, 366504424366080, 14515574208519384, 612912858447052800, 27497080096591516320, 1306520704652165775360, 65556843230110158804960, 3464412427539012262035456

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=5 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+5)*(i-1)!^j*
      multinomial(n, n-i*j, i$j)/j!, j=0..n/i)))
    end:
a:= a->add(b(j, 5)*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..25);

Mathematica

CoefficientList[Series[1/(1+LambertW[-x]^5)^(1/5),{x,0,20}],x] * Range[0,20]!  (* Vaclav Kotesovec, Sep 01 2014 *)

Formula

E.g.f.: 1/(1+LambertW(-x)^5)^(1/5). - Vaclav Kotesovec, Sep 01 2014

a(n) ~ n^(n-2/5) * 2^(2/5) * (sqrt(Pi) / (5^(1/5) * Gamma(1/10))) * (1 - 14 * sqrt(2/n) * Gamma(1/10) / (75 * Gamma(3/5))). - Vaclav Kotesovec, Sep 01 2014