A245982 - OEIS

%I #4 Aug 09 2014 11:44:42

%S 1,1,6,87,2200,159245,22460976,3841485235,725338311552,

%T 150719206127769,35342379764876800,9829163373723941951,

%U 3429714088052022223872,1523614487096970692512933,823050850772773045911871488,507838824721407879972472444875

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

%H Alois P. Heinz, <a href="/A245982/b245982.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, 5],

%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=5 of A245980.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Aug 08 2014