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A245987 Number of pairs of endofunctions f, g on [n] satisfying g^10(f(i)) = f(i) for all i in [n].

%I A245987 #4 Aug 09 2014 12:46:26
%S A245987 1,1,10,213,8056,540945,55791936,7976641981,1469902760320,
%T A245987 332703236420577,93998774487116800,34310097895273565541,
%U A245987 16097501586129903138816,9217140995822760715385905,6076268404868213191347785728,4448129862114255651329796526125
%N A245987 Number of pairs of endofunctions f, g on [n] satisfying g^10(f(i)) = f(i) for all i in [n].
%H A245987 Alois P. Heinz, <a href="/A245987/b245987.txt">Table of n, a(n) for n = 0..100</a>
%p A245987 with(combinat): M:=multinomial:
%p A245987 b:= proc(n, k) local l, g; l, g:= [1, 2, 5, 10],
%p A245987       proc(k, m, i, t) option remember; local d, j; d:= l[i];
%p A245987         `if`(i=1, n^m, add(M(k, k-(d-t)*j, (d-t)$j)/j!*
%p A245987          (d-1)!^j *M(m, m-t*j, t$j) *g(k-(d-t)*j, m-t*j,
%p A245987         `if`(d-t=1, [i-1, 0], [i, t+1])[]), j=0..min(k/(d-t),
%p A245987         `if`(t=0, [][], m/t))))
%p A245987       end; g(k, n-k, nops(l), 0)
%p A245987     end:
%p A245987 a:= n-> add(b(n, j)*stirling2(n, j)*binomial(n, j)*j!, j=0..n):
%p A245987 seq(a(n), n=0..20);
%Y A245987 Column k=10 of A245980.
%K A245987 nonn
%O A245987 0,3
%A A245987 _Alois P. Heinz_, Aug 08 2014