A245982 Number of pairs of endofunctions f, g on [n] satisfying g^5(f(i)) = f(i) for all i in [n].

1, 1, 6, 87, 2200, 159245, 22460976, 3841485235, 725338311552, 150719206127769, 35342379764876800, 9829163373723941951, 3429714088052022223872, 1523614487096970692512933, 823050850772773045911871488, 507838824721407879972472444875

Offset: 0

Author

Alois P. Heinz, Aug 08 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..100

Crossrefs

Column k=5 of A245980.

Programs

Maple

with(combinat): M:=multinomial:
b:= proc(n, k) local l, g; l, g:= [1, 5],
      proc(k, m, i, t) option remember; local d, j; d:= l[i];
        `if`(i=1, n^m, add(M(k, k-(d-t)*j, (d-t)$j)/j!*
         (d-1)!^j *M(m, m-t*j, t$j) *g(k-(d-t)*j, m-t*j,
        `if`(d-t=1, [i-1, 0], [i, t+1])[]), j=0..min(k/(d-t),
        `if`(t=0, [][], m/t))))
      end; g(k, n-k, nops(l), 0)
    end:
a:= n-> add(b(n, j)*stirling2(n, j)*binomial(n, j)*j!, j=0..n):
seq(a(n), n=0..20);