A247008 Number of permutations on [n] admitting a tenth root.

1, 1, 1, 3, 12, 36, 126, 1386, 10248, 92232, 805896, 9862776, 107908416, 1428755328, 17338793472, 184781653056, 2707269941376, 58956779097216, 931404051946368, 18440063711701632, 369535355215842816, 8290691125502962176, 161390500012170164736

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=10 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(10, 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);