A245912 - OEIS

%I #5 Aug 06 2014 15:14:07

%S 1,1,10,207,6856,302345,17812656,1384059775,131612023936,

%T 14986421437329,2051598980742400,327546779949753551,

%U 59790068922261980160,12505503377433451819993,2956768061598853524176896,778675046844529953944661375,228393818322135051214683406336

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

%H Alois P. Heinz, <a href="/A245912/b245912.txt">Table of n, a(n) for n = 0..150</a>

%p with(combinat):

%p T:= proc(n, j) option remember; binomial(n-1, j-1)*n^(n-j) end:

%p b:= proc(n, i) option remember; `if`(n=0 or i=1, x^n,

%p       expand(add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*

%p       x^(igcd(i, 3)*j)*b(n-i*j, i-1), j=0..n/i)))

%p     end:

%p a:= n-> add((p-> add(n^i*T(n, j)* coeff(p, x, i),

%p         i=0..degree(p)))(b(j$2)), j=0..n):

%p seq(a(n), n=0..20);

%Y Column k=3 of A245910.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Aug 06 2014