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A246197 Number of endofunctions on [n] where the smallest cycle length equals 10.

%I A246197 #9 Aug 21 2014 05:45:58
%S A246197 362880,39916800,2874009600,175394419200,9967384627200,
%T A246197 551675124000000,30471021291110400,1703458301210265600,
%U A246197 97213825272736972800,5693251850259515942400,343266609438110040883200,21349182724237331665228800,1371132989012608561874534400
%N A246197 Number of endofunctions on [n] where the smallest cycle length equals 10.
%C A246197 In general, number of endofunctions on [n] where the smallest cycle length equals k is asymptotic to (exp(-H(k-1)) - exp(-H(k))) * n^n, where H(k) is the harmonic number A001008/A002805, k>=1. - _Vaclav Kotesovec_, Aug 21 2014
%H A246197 Alois P. Heinz, <a href="/A246197/b246197.txt">Table of n, a(n) for n = 10..200</a>
%F A246197 a(n) ~ (exp(-7129/2520) - exp(-7381/2520))* n^n. - _Vaclav Kotesovec_, Aug 21 2014
%p A246197 with(combinat):
%p A246197 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>n, 0,
%p A246197       add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
%p A246197       b(n-i*j, i+1), j=0..n/i)))
%p A246197     end:
%p A246197 A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, k), j=0..n):
%p A246197 a:= n-> A(n, 10) -A(n, 11):
%p A246197 seq(a(n), n=10..25);
%Y A246197 Column k=10 of A246049.
%K A246197 nonn
%O A246197 10,1
%A A246197 _Alois P. Heinz_, Aug 18 2014