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A246614
Number of endofunctions on [n] whose cycle lengths are multiples of 7.
2
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 31 2014
STATUS
approved