cp's OEIS Frontend

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

%I A247007 #4 Sep 09 2014 07:58:00
%S A247007 1,1,2,4,16,80,400,2800,22400,179200,1792000,19712000,216832000,
%T A247007 2818816000,39463424000,552487936000,8839806976000,150276718592000,
%U A247007 2554704216064000,48539380105216000,970787602104320000,19415752042086400000,427146544925900800000,9824370533295718400000,225960522265801523200000,5649013056645038080000000,146874339472770990080000000,3818732827816549381939200000
%N A247007 Number of permutations on [n] admitting a ninth root.
%C A247007 Differs from A102736 first at n=27.
%H A247007 Alois P. Heinz, <a href="/A247007/b247007.txt">Table of n, a(n) for n = 0..300</a>
%H A247007 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 A247007 with(combinat): with(numtheory): with(padic):
%p A247007 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
%p A247007       `if`(irem(j, mul(p^ordp(9, p), p=factorset(i)))=0, (i-1)!^j*
%p A247007       multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1), 0), j=0..n/i)))
%p A247007     end:
%p A247007 a:= n-> b(n$2):
%p A247007 seq(a(n), n=0..27);
%Y A247007 Column k=9 of A247005.
%K A247007 nonn
%O A247007 0,3
%A A247007 _Alois P. Heinz_, Sep 09 2014