cp's OEIS Frontend

A245913 Number of pairs of endofunctions f, g on [n] satisfying f(g^4(i)) = f(i) for all i in [n].

%I A245913 #4 Aug 06 2014 15:15:17
%S A245913 1,1,12,249,9184,488745,35463456,3212948809,369653885952,
%T A245913 52089606360081,8863922597593600,1752215974571247801,
%U A245913 402913941534323970048,106177876504463493003001,31939024924944619647750144,10756222724503803551432639625,4050020577581980281160989147136
%N A245913 Number of pairs of endofunctions f, g on [n] satisfying f(g^4(i)) = f(i) for all i in [n].
%H A245913 Alois P. Heinz, <a href="/A245913/b245913.txt">Table of n, a(n) for n = 0..150</a>
%p A245913 with(combinat):
%p A245913 T:= proc(n, j) option remember; binomial(n-1, j-1)*n^(n-j) end:
%p A245913 b:= proc(n, i) option remember; `if`(n=0 or i=1, x^n,
%p A245913       expand(add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
%p A245913       x^(igcd(i, 4)*j)*b(n-i*j, i-1), j=0..n/i)))
%p A245913     end:
%p A245913 a:= n-> add((p-> add(n^i*T(n, j)* coeff(p, x, i),
%p A245913         i=0..degree(p)))(b(j$2)), j=0..n):
%p A245913 seq(a(n), n=0..20);
%Y A245913 Column k=4 of A245910.
%K A245913 nonn
%O A245913 0,3
%A A245913 _Alois P. Heinz_, Aug 06 2014