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

0,6

Links

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

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

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 *)

Crossrefs

Column k=5 of A246609.

Sequence in context: A093456 A189412 A246192 * A289635 A105187 A062313

Adjacent sequences: A246609 A246610 A246611 * A246613 A246614 A246615

Keyword

nonn

Author

Alois P. Heinz, Aug 31 2014

Status

approved