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A246612 Number of endofunctions on [n] whose cycle lengths are multiples of 5. 2

%I

%S 1,0,0,0,0,24,720,17640,430080,11022480,302835456,8976567600,

%T 287236730880,9901354268520,366504424366080,14515574208519384,

%U 612912858447052800,27497080096591516320,1306520704652165775360,65556843230110158804960,3464412427539012262035456

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

%H Alois P. Heinz, <a href="/A246612/b246612.txt">Table of n, a(n) for n = 0..300</a>

%F E.g.f.: 1/(1+LambertW(-x)^5)^(1/5). - _Vaclav Kotesovec_, Sep 01 2014

%F 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

%p with(combinat):

%p b:= proc(n, i) option remember; `if`(n=0, 1,

%p `if`(i>n, 0, add(b(n-i*j, i+5)*(i-1)!^j*

%p multinomial(n, n-i*j, i$j)/j!, j=0..n/i)))

%p end:

%p a:= a->add(b(j, 5)*n^(n-j)*binomial(n-1, j-1), j=0..n):

%p seq(a(n), n=0..25);

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

%Y Column k=5 of A246609.

%K nonn

%O 0,6

%A _Alois P. Heinz_, Aug 31 2014

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Last modified January 17 04:46 EST 2022. Contains 350378 sequences. (Running on oeis4.)