A245917 Number of pairs of endofunctions f, g on [n] satisfying f(g^8(i)) = f(i) for all i in [n].

1, 1, 12, 249, 9184, 488745, 35463456, 3212948809, 454190410752, 85278734539281, 19295679317593600, 4754101825771791801, 1391380506872608002048, 467080657604802224657401, 177425478031159409407340544, 72694051770982862424632639625

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=8 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, 8)*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);