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

1, 1, 10, 213, 9592, 682545, 69119136, 9284636221, 1597922254720, 344058384011553, 90769698354764800, 28762381447366581861, 10751918763610399942656, 4671451080680229243978385, 2331208959412708894563057664, 1323549917511104579568688414125

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=4 of A245980.

Programs

Maple

with(combinat): M:=multinomial:
b:= proc(n, k) local l, g; l, g:= [1, 2, 4],
      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);