cp's OEIS Frontend

A245986 Number of pairs of endofunctions f, g on [n] satisfying g^9(f(i)) = f(i) for all i in [n].

%I A245986 #4 Aug 09 2014 12:34:54
%S A245986 1,1,6,141,6184,387545,33404256,3891981205,592320594048,
%T A245986 128805405787953,43012267760166400,19329826195760619341,
%U A245986 10086545470056599549952,5787171311384573282516617,3623228151360430287454531584,2480483584581055916081566933125
%N A245986 Number of pairs of endofunctions f, g on [n] satisfying g^9(f(i)) = f(i) for all i in [n].
%H A245986 Alois P. Heinz, <a href="/A245986/b245986.txt">Table of n, a(n) for n = 0..100</a>
%p A245986 with(combinat): M:=multinomial:
%p A245986 b:= proc(n, k) local l, g; l, g:= [1, 3, 9],
%p A245986       proc(k, m, i, t) option remember; local d, j; d:= l[i];
%p A245986         `if`(i=1, n^m, add(M(k, k-(d-t)*j, (d-t)$j)/j!*
%p A245986          (d-1)!^j *M(m, m-t*j, t$j) *g(k-(d-t)*j, m-t*j,
%p A245986         `if`(d-t=1, [i-1, 0], [i, t+1])[]), j=0..min(k/(d-t),
%p A245986         `if`(t=0, [][], m/t))))
%p A245986       end; g(k, n-k, nops(l), 0)
%p A245986     end:
%p A245986 a:= n-> add(b(n, j)*stirling2(n, j)*binomial(n, j)*j!, j=0..n):
%p A245986 seq(a(n), n=0..20);
%Y A245986 Column k=9 of A245980.
%K A245986 nonn
%O A245986 0,3
%A A245986 _Alois P. Heinz_, Aug 08 2014