cp's OEIS Frontend

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

%I A247008 #4 Sep 09 2014 07:48:40
%S A247008 1,1,1,3,12,36,126,1386,10248,92232,805896,9862776,107908416,
%T A247008 1428755328,17338793472,184781653056,2707269941376,58956779097216,
%U A247008 931404051946368,18440063711701632,369535355215842816,8290691125502962176,161390500012170164736
%N A247008 Number of permutations on [n] admitting a tenth root.
%H A247008 Alois P. Heinz, <a href="/A247008/b247008.txt">Table of n, a(n) for n = 0..300</a>
%H A247008 H. S. Wilf, <a href="http://www.math.upenn.edu/~wilf/DownldGF.html">Generatingfunctionology</a>, 2nd edn., Academic Press, NY, 1994, Theorem 4.8.2.
%p A247008 with(combinat): with(numtheory): with(padic):
%p A247008 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
%p A247008       `if`(irem(j, mul(p^ordp(10, p), p=factorset(i)))=0, (i-1)!^j*
%p A247008       multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1), 0), j=0..n/i)))
%p A247008     end:
%p A247008 a:= n-> b(n$2):
%p A247008 seq(a(n), n=0..25);
%Y A247008 Column k=10 of A247005.
%K A247008 nonn
%O A247008 0,4
%A A247008 _Alois P. Heinz_, Sep 09 2014