cp's OEIS Frontend

A245981 Number of pairs of endofunctions f, g on [n] satisfying g^4(f(i)) = f(i) for all i in [n].

%I A245981 #6 Aug 09 2014 11:18:25
%S A245981 1,1,10,213,9592,682545,69119136,9284636221,1597922254720,
%T A245981 344058384011553,90769698354764800,28762381447366581861,
%U A245981 10751918763610399942656,4671451080680229243978385,2331208959412708894563057664,1323549917511104579568688414125
%N A245981 Number of pairs of endofunctions f, g on [n] satisfying g^4(f(i)) = f(i) for all i in [n].
%H A245981 Alois P. Heinz, <a href="/A245981/b245981.txt">Table of n, a(n) for n = 0..100</a>
%p A245981 with(combinat): M:=multinomial:
%p A245981 b:= proc(n, k) local l, g; l, g:= [1, 2, 4],
%p A245981       proc(k, m, i, t) option remember; local d, j; d:= l[i];
%p A245981         `if`(i=1, n^m, add(M(k, k-(d-t)*j, (d-t)$j)/j!*
%p A245981          (d-1)!^j *M(m, m-t*j, t$j) *g(k-(d-t)*j, m-t*j,
%p A245981         `if`(d-t=1, [i-1, 0], [i, t+1])[]), j=0..min(k/(d-t),
%p A245981         `if`(t=0, [][], m/t))))
%p A245981       end; g(k, n-k, nops(l), 0)
%p A245981     end:
%p A245981 a:= n-> add(b(n, j)*stirling2(n, j)*binomial(n, j)*j!, j=0..n):
%p A245981 seq(a(n), n=0..20);
%Y A245981 Column k=4 of A245980.
%K A245981 nonn
%O A245981 0,3
%A A245981 _Alois P. Heinz_, Aug 08 2014