cp's OEIS Frontend

A245912 Number of pairs of endofunctions f, g on [n] satisfying f(g^3(i)) = f(i) for all i in [n].

%I A245912 #5 Aug 06 2014 15:14:07
%S A245912 1,1,10,207,6856,302345,17812656,1384059775,131612023936,
%T A245912 14986421437329,2051598980742400,327546779949753551,
%U A245912 59790068922261980160,12505503377433451819993,2956768061598853524176896,778675046844529953944661375,228393818322135051214683406336
%N A245912 Number of pairs of endofunctions f, g on [n] satisfying f(g^3(i)) = f(i) for all i in [n].
%H A245912 Alois P. Heinz, <a href="/A245912/b245912.txt">Table of n, a(n) for n = 0..150</a>
%p A245912 with(combinat):
%p A245912 T:= proc(n, j) option remember; binomial(n-1, j-1)*n^(n-j) end:
%p A245912 b:= proc(n, i) option remember; `if`(n=0 or i=1, x^n,
%p A245912       expand(add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
%p A245912       x^(igcd(i, 3)*j)*b(n-i*j, i-1), j=0..n/i)))
%p A245912     end:
%p A245912 a:= n-> add((p-> add(n^i*T(n, j)* coeff(p, x, i),
%p A245912         i=0..degree(p)))(b(j$2)), j=0..n):
%p A245912 seq(a(n), n=0..20);
%Y A245912 Column k=3 of A245910.
%K A245912 nonn
%O A245912 0,3
%A A245912 _Alois P. Heinz_, Aug 06 2014