cp's OEIS Frontend

A245916 Number of pairs of endofunctions f, g on [n] satisfying f(g^7(i)) = f(i) for all i in [n].

%I A245916 #4 Aug 06 2014 15:29:21
%S A245916 1,1,10,159,3496,98345,3373056,729481375,187564765312,37157158911249,
%T A245916 6404841810150400,1033733019005497151,162392131536566261760,
%U A245916 25373998461297751027321,13879265226159974639036416,11935104515280353051806269375,7611603822558997773619173031936
%N A245916 Number of pairs of endofunctions f, g on [n] satisfying f(g^7(i)) = f(i) for all i in [n].
%H A245916 Alois P. Heinz, <a href="/A245916/b245916.txt">Table of n, a(n) for n = 0..150</a>
%p A245916 with(combinat):
%p A245916 b:= proc(n, i) option remember; unapply(`if`(n=0 or i=1, x^n,
%p A245916       expand(add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
%p A245916       x^(igcd(i, 7)*j)*b(n-i*j, i-1)(x), j=0..n/i))), x)
%p A245916     end:
%p A245916 a:= n-> add(binomial(n-1, j-1)*n^(n-j)*b(j$2)(n), j=0..n):
%p A245916 seq(a(n), n=0..20);
%Y A245916 Column k=7 of A245910.
%K A245916 nonn
%O A245916 0,3
%A A245916 _Alois P. Heinz_, Aug 06 2014