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A246612 Number of endofunctions on [n] whose cycle lengths are multiples of 5. 2
1, 0, 0, 0, 0, 24, 720, 17640, 430080, 11022480, 302835456, 8976567600, 287236730880, 9901354268520, 366504424366080, 14515574208519384, 612912858447052800, 27497080096591516320, 1306520704652165775360, 65556843230110158804960, 3464412427539012262035456 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 28 08:12 EST 2021. Contains 349401 sequences. (Running on oeis4.)