A247007 Number of permutations on [n] admitting a ninth root.

1, 1, 2, 4, 16, 80, 400, 2800, 22400, 179200, 1792000, 19712000, 216832000, 2818816000, 39463424000, 552487936000, 8839806976000, 150276718592000, 2554704216064000, 48539380105216000, 970787602104320000, 19415752042086400000, 427146544925900800000, 9824370533295718400000, 225960522265801523200000, 5649013056645038080000000, 146874339472770990080000000, 3818732827816549381939200000

Offset

0,3

Comments

Differs from A102736 first at n=27.

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(9, 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..27);

Crossrefs

Column k=9 of A247005.

Sequence in context: A340900 A347631 A102736 * A103619 A027436 A025225

Adjacent sequences: A247004 A247005 A247006 * A247008 A247009 A247010

Keyword

nonn

Author

Alois P. Heinz, Sep 09 2014

Status

approved