login
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
OFFSET
0,6
LINKS
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 31 2014
STATUS
approved