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

0,4

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.

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);

Crossrefs

Column k=8 of A247005.

Sequence in context: A262134 A262135 A000246 * A103620 A138315 A337849

Adjacent sequences: A247003 A247004 A247005 * A247007 A247008 A247009

Keyword

nonn

Author

Alois P. Heinz, Sep 09 2014

Status

approved