cp's OEIS Frontend

A245918 Number of pairs of endofunctions f, g on [n] satisfying f(g^9(i)) = f(i) for all i in [n].

%I A245918 #4 Aug 06 2014 15:42:43
%S A245918 1,1,10,207,6856,302345,17812656,1384059775,131612023936,
%T A245918 30607186160529,9712391319942400,2685817593368889551,
%U A245918 809491207939940828160,280106645752842329055193,99175751774345673351479296,36958774352800067430488661375,15213494922728791702295969038336
%N A245918 Number of pairs of endofunctions f, g on [n] satisfying f(g^9(i)) = f(i) for all i in [n].
%H A245918 Alois P. Heinz, <a href="/A245918/b245918.txt">Table of n, a(n) for n = 0..150</a>
%p A245918 with(combinat):
%p A245918 b:= proc(n, i) option remember; unapply(`if`(n=0 or i=1, x^n,
%p A245918       expand(add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
%p A245918       x^(igcd(i, 9)*j)*b(n-i*j, i-1)(x), j=0..n/i))), x)
%p A245918     end:
%p A245918 a:= n-> add(binomial(n-1, j-1)*n^(n-j)*b(j$2)(n), j=0..n):
%p A245918 seq(a(n), n=0..20);
%Y A245918 Column k=9 of A245910.
%K A245918 nonn
%O A245918 0,3
%A A245918 _Alois P. Heinz_, Aug 06 2014