cp's OEIS Frontend

A245985 Number of pairs of endofunctions f, g on [n] satisfying g^8(f(i)) = f(i) for all i in [n].

%I A245985 #6 Aug 09 2014 12:26:09
%S A245985 1,1,10,213,9592,682545,69119136,9284636221,1682479423360,
%T A245985 410336706483873,129022118179494400,49380786699038009061,
%U A245985 22121770547251791968256,11386670423628468306437905,6678552357682831880750669824,4435028805132706191344837902125
%N A245985 Number of pairs of endofunctions f, g on [n] satisfying g^8(f(i)) = f(i) for all i in [n].
%H A245985 Alois P. Heinz, <a href="/A245985/b245985.txt">Table of n, a(n) for n = 0..100</a>
%p A245985 with(combinat): M:=multinomial:
%p A245985 b:= proc(n, k) local l, g; l, g:= [1, 2, 4, 8],
%p A245985       proc(k, m, i, t) option remember; local d, j; d:= l[i];
%p A245985         `if`(i=1, n^m, add(M(k, k-(d-t)*j, (d-t)$j)/j!*
%p A245985          (d-1)!^j *M(m, m-t*j, t$j) *g(k-(d-t)*j, m-t*j,
%p A245985         `if`(d-t=1, [i-1, 0], [i, t+1])[]), j=0..min(k/(d-t),
%p A245985         `if`(t=0, [][], m/t))))
%p A245985       end; g(k, n-k, nops(l), 0)
%p A245985     end:
%p A245985 a:= n-> add(b(n, j)*stirling2(n, j)*binomial(n, j)*j!, j=0..n):
%p A245985 seq(a(n), n=0..20);
%Y A245985 Column k=8 of A245980.
%K A245985 nonn
%O A245985 0,3
%A A245985 _Alois P. Heinz_, Aug 08 2014