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A245983 Number of pairs of endofunctions f, g on [n] satisfying g^6(f(i)) = f(i) for all i in [n].

%I A245983 #5 Aug 09 2014 12:08:40
%S A245983 1,1,10,267,12040,826245,86252976,12661148311,2428606888576,
%T A245983 585229569018921,172640322717932800,60933514918456147011,
%U A245983 25283156000087876668416,12189356237264450125373869,6769905753950075837079906304,4297777320612236566890778059375
%N A245983 Number of pairs of endofunctions f, g on [n] satisfying g^6(f(i)) = f(i) for all i in [n].
%H A245983 Alois P. Heinz, <a href="/A245983/b245983.txt">Table of n, a(n) for n = 0..100</a>
%p A245983 with(combinat): M:=multinomial:
%p A245983 b:= proc(n, k) local l, g; l, g:= [1, 2, 3, 6],
%p A245983       proc(k, m, i, t) option remember; local d, j; d:= l[i];
%p A245983         `if`(i=1, n^m, add(M(k, k-(d-t)*j, (d-t)$j)/j!*
%p A245983          (d-1)!^j *M(m, m-t*j, t$j) *g(k-(d-t)*j, m-t*j,
%p A245983         `if`(d-t=1, [i-1, 0], [i, t+1])[]), j=0..min(k/(d-t),
%p A245983         `if`(t=0, [][], m/t))))
%p A245983       end; g(k, n-k, nops(l), 0)
%p A245983     end:
%p A245983 a:= n->add(b(n, j)*stirling2(n, j)*binomial(n, j)*j!, j=0..n):
%p A245983 seq(a(n), n=0..20);
%Y A245983 Column k=6 of A245980.
%K A245983 nonn
%O A245983 0,3
%A A245983 _Alois P. Heinz_, Aug 08 2014