A247006 Number of permutations on [n] admitting an eighth root.

1, 1, 1, 3, 9, 45, 225, 1575, 11025, 99225, 893025, 9823275, 108056025, 1404728325, 18261468225, 273922023375, 4108832377650, 69850150420050, 1187452281465450, 22561593347843550, 428670250038780750, 9002075250814395750, 189043575317350503750

Offset: 0

Author

Alois P. Heinz, Sep 09 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..300
• H. S. Wilf, Generatingfunctionology, 2nd edn., Academic Press, NY, 1994, Theorem 4.8.2.

Crossrefs

Column k=8 of A247005.

Programs

Maple

with(combinat): with(numtheory): with(padic):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
      `if`(irem(j, mul(p^ordp(8, p), p=factorset(i)))=0, (i-1)!^j*
      multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1), 0), j=0..n/i)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..25);