A246614 - OEIS

%I #13 Jun 11 2024 01:38:56

%S 1,0,0,0,0,0,0,720,40320,1632960,60480000,2213719200,82771476480,

%T 3211179491520,130247609057280,5542874078742000,247828800444825600,

%U 11643316737494682240,574455837701776343040,29734324379435446505280,1612668074301849600000000

%N Number of endofunctions on [n] whose cycle lengths are multiples of 7.

%H Alois P. Heinz, <a href="/A246614/b246614.txt">Table of n, a(n) for n = 0..300</a>

%F E.g.f.: 1/(1+LambertW(-x)^7)^(1/7). - _Vaclav Kotesovec_, Sep 01 2014

%F 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

%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+7)*(i-1)!^j*

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

%p     end:

%p a:= a->add(b(j, 7)*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]^7)^(1/7),{x,0,20}],x] * Range[0,20]!  (* _Vaclav Kotesovec_, Sep 01 2014 *)

%Y Column k=7 of A246609.

%K nonn

%O 0,8

%A _Alois P. Heinz_, Aug 31 2014