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

0,4

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(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);

Crossrefs

Column k=10 of A247005.

Sequence in context: A290927 A167993 A061130 * A344062 A303308 A155714

Adjacent sequences: A247005 A247006 A247007 * A247009 A247010 A247011

Keyword

nonn

Author

Alois P. Heinz, Sep 09 2014

Status

approved