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A245982 Number of pairs of endofunctions f, g on [n] satisfying g^5(f(i)) = f(i) for all i in [n].

%I A245982 #4 Aug 09 2014 11:44:42
%S A245982 1,1,6,87,2200,159245,22460976,3841485235,725338311552,
%T A245982 150719206127769,35342379764876800,9829163373723941951,
%U A245982 3429714088052022223872,1523614487096970692512933,823050850772773045911871488,507838824721407879972472444875
%N A245982 Number of pairs of endofunctions f, g on [n] satisfying g^5(f(i)) = f(i) for all i in [n].
%H A245982 Alois P. Heinz, <a href="/A245982/b245982.txt">Table of n, a(n) for n = 0..100</a>
%p A245982 with(combinat): M:=multinomial:
%p A245982 b:= proc(n, k) local l, g; l, g:= [1, 5],
%p A245982       proc(k, m, i, t) option remember; local d, j; d:= l[i];
%p A245982         `if`(i=1, n^m, add(M(k, k-(d-t)*j, (d-t)$j)/j!*
%p A245982          (d-1)!^j *M(m, m-t*j, t$j) *g(k-(d-t)*j, m-t*j,
%p A245982         `if`(d-t=1, [i-1, 0], [i, t+1])[]), j=0..min(k/(d-t),
%p A245982         `if`(t=0, [][], m/t))))
%p A245982       end; g(k, n-k, nops(l), 0)
%p A245982     end:
%p A245982 a:= n-> add(b(n, j)*stirling2(n, j)*binomial(n, j)*j!, j=0..n):
%p A245982 seq(a(n), n=0..20);
%Y A245982 Column k=5 of A245980.
%K A245982 nonn
%O A245982 0,3
%A A245982 _Alois P. Heinz_, Aug 08 2014