login
Number of pairs of endofunctions f, g on [n] satisfying f(g^8(i)) = f(i) for all i in [n].
2

%I #4 Aug 06 2014 15:36:22

%S 1,1,12,249,9184,488745,35463456,3212948809,454190410752,

%T 85278734539281,19295679317593600,4754101825771791801,

%U 1391380506872608002048,467080657604802224657401,177425478031159409407340544,72694051770982862424632639625

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

%H Alois P. Heinz, <a href="/A245917/b245917.txt">Table of n, a(n) for n = 0..150</a>

%p with(combinat):

%p b:= proc(n, i) option remember; unapply(`if`(n=0 or i=1, x^n,

%p expand(add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*

%p x^(igcd(i, 8)*j)*b(n-i*j, i-1)(x), j=0..n/i))), x)

%p end:

%p a:= n-> add(binomial(n-1, j-1)*n^(n-j)*b(j$2)(n), j=0..n):

%p seq(a(n), n=0..20);

%Y Column k=8 of A245910.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Aug 06 2014