A245916 Number of pairs of endofunctions f, g on [n] satisfying f(g^7(i)) = f(i) for all i in [n].

1, 1, 10, 159, 3496, 98345, 3373056, 729481375, 187564765312, 37157158911249, 6404841810150400, 1033733019005497151, 162392131536566261760, 25373998461297751027321, 13879265226159974639036416, 11935104515280353051806269375, 7611603822558997773619173031936

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=7 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, 7)*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);