A245914 - OEIS

%I #5 Aug 06 2014 15:15:48

%S 1,1,10,159,3496,173225,15680736,1618295455,169456569472,

%T 17962132149009,2673715009888000,652752279443748671,

%U 185425990150444922880,50400836024570702513401,12815973354809222836596736,3862679850655546273674429375,1722827488179450551983866413056

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

%H Alois P. Heinz, <a href="/A245914/b245914.txt">Table of n, a(n) for n = 0..150</a>

%p with(combinat):

%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, 5)*j)*b(n-i*j, i-1), j=0..n/i)))

%p     end:

%p a:= n-> add(binomial(n-1, j-1)*n^(n-j)*subs(x=n, b(j$2)), j=0..n):

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

%Y Column k=5 of A245910.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Aug 06 2014