A245981 - OEIS

%I #6 Aug 09 2014 11:18:25

%S 1,1,10,213,9592,682545,69119136,9284636221,1597922254720,

%T 344058384011553,90769698354764800,28762381447366581861,

%U 10751918763610399942656,4671451080680229243978385,2331208959412708894563057664,1323549917511104579568688414125

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

%H Alois P. Heinz, <a href="/A245981/b245981.txt">Table of n, a(n) for n = 0..100</a>

%p with(combinat): M:=multinomial:

%p b:= proc(n, k) local l, g; l, g:= [1, 2, 4],

%p       proc(k, m, i, t) option remember; local d, j; d:= l[i];

%p         `if`(i=1, n^m, add(M(k, k-(d-t)*j, (d-t)$j)/j!*

%p          (d-1)!^j *M(m, m-t*j, t$j) *g(k-(d-t)*j, m-t*j,

%p         `if`(d-t=1, [i-1, 0], [i, t+1])[]), j=0..min(k/(d-t),

%p         `if`(t=0, [][], m/t))))

%p       end; g(k, n-k, nops(l), 0)

%p     end:

%p a:= n-> add(b(n, j)*stirling2(n, j)*binomial(n, j)*j!, j=0..n):

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

%Y Column k=4 of A245980.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Aug 08 2014