A245918 Number of pairs of endofunctions f, g on [n] satisfying f(g^9(i)) = f(i) for all i in [n].

1, 1, 10, 207, 6856, 302345, 17812656, 1384059775, 131612023936, 30607186160529, 9712391319942400, 2685817593368889551, 809491207939940828160, 280106645752842329055193, 99175751774345673351479296, 36958774352800067430488661375, 15213494922728791702295969038336

Offset: 0

Author

Alois P. Heinz, Aug 06 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..150

Crossrefs

Column k=9 of A245910.

Programs

Maple

with(combinat):
b:= proc(n, i) option remember; unapply(`if`(n=0 or i=1, x^n,
      expand(add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
      x^(igcd(i, 9)*j)*b(n-i*j, i-1)(x), j=0..n/i))), x)
    end:
a:= n-> add(binomial(n-1, j-1)*n^(n-j)*b(j$2)(n), j=0..n):
seq(a(n), n=0..20);