A245914 Number of pairs of endofunctions f, g on [n] satisfying f(g^5(i)) = f(i) for all i in [n].

1, 1, 10, 159, 3496, 173225, 15680736, 1618295455, 169456569472, 17962132149009, 2673715009888000, 652752279443748671, 185425990150444922880, 50400836024570702513401, 12815973354809222836596736, 3862679850655546273674429375, 1722827488179450551983866413056

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=5 of A245910.

Programs

Maple

with(combinat):
b:= proc(n, i) option remember; `if`(n=0 or i=1, x^n,
      expand(add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
      x^(igcd(i, 5)*j)*b(n-i*j, i-1), j=0..n/i)))
    end:
a:= n-> add(binomial(n-1, j-1)*n^(n-j)*subs(x=n, b(j$2)), j=0..n):
seq(a(n), n=0..20);