cp's OEIS Frontend

A245914 Number of pairs of endofunctions f, g on [n] satisfying f(g^5(i)) = f(i) for all i in [n].

%I A245914 #5 Aug 06 2014 15:15:48
%S A245914 1,1,10,159,3496,173225,15680736,1618295455,169456569472,
%T A245914 17962132149009,2673715009888000,652752279443748671,
%U A245914 185425990150444922880,50400836024570702513401,12815973354809222836596736,3862679850655546273674429375,1722827488179450551983866413056
%N A245914 Number of pairs of endofunctions f, g on [n] satisfying f(g^5(i)) = f(i) for all i in [n].
%H A245914 Alois P. Heinz, <a href="/A245914/b245914.txt">Table of n, a(n) for n = 0..150</a>
%p A245914 with(combinat):
%p A245914 b:= proc(n, i) option remember; `if`(n=0 or i=1, x^n,
%p A245914       expand(add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
%p A245914       x^(igcd(i, 5)*j)*b(n-i*j, i-1), j=0..n/i)))
%p A245914     end:
%p A245914 a:= n-> add(binomial(n-1, j-1)*n^(n-j)*subs(x=n, b(j$2)), j=0..n):
%p A245914 seq(a(n), n=0..20);
%Y A245914 Column k=5 of A245910.
%K A245914 nonn
%O A245914 0,3
%A A245914 _Alois P. Heinz_, Aug 06 2014