cp's OEIS Frontend

A245917 Number of pairs of endofunctions f, g on [n] satisfying f(g^8(i)) = f(i) for all i in [n].

%I A245917 #4 Aug 06 2014 15:36:22
%S A245917 1,1,12,249,9184,488745,35463456,3212948809,454190410752,
%T A245917 85278734539281,19295679317593600,4754101825771791801,
%U A245917 1391380506872608002048,467080657604802224657401,177425478031159409407340544,72694051770982862424632639625
%N A245917 Number of pairs of endofunctions f, g on [n] satisfying f(g^8(i)) = f(i) for all i in [n].
%H A245917 Alois P. Heinz, <a href="/A245917/b245917.txt">Table of n, a(n) for n = 0..150</a>
%p A245917 with(combinat):
%p A245917 b:= proc(n, i) option remember; unapply(`if`(n=0 or i=1, x^n,
%p A245917       expand(add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
%p A245917       x^(igcd(i, 8)*j)*b(n-i*j, i-1)(x), j=0..n/i))), x)
%p A245917     end:
%p A245917 a:= n-> add(binomial(n-1, j-1)*n^(n-j)*b(j$2)(n), j=0..n):
%p A245917 seq(a(n), n=0..20);
%Y A245917 Column k=8 of A245910.
%K A245917 nonn
%O A245917 0,3
%A A245917 _Alois P. Heinz_, Aug 06 2014