A245984 Number of pairs of endofunctions f, g on [n] satisfying g^7(f(i)) = f(i) for all i in [n].

1, 1, 6, 87, 2200, 84245, 4492656, 908888155, 357260391552, 135745499491209, 49743738690284800, 18418196210352315311, 7088670872640238205952, 2879857079508362958098653, 1254944121383140772128247808, 610054332530467361553695923875

Offset

0,3

Links

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

Maple

with(combinat): M:=multinomial:
b:= proc(n, k) local l, g; l, g:= [1, 7],
      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);

Crossrefs

Column k=7 of A245980.

Sequence in context: A138216 A294491 A239750 * A245982 A294045 A171207

Adjacent sequences: A245981 A245982 A245983 * A245985 A245986 A245987

Keyword

nonn

Author

Alois P. Heinz, Aug 08 2014

Status

approved