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A247006 Number of permutations on [n] admitting an eighth root.

%I A247006 #6 Sep 09 2014 07:54:16
%S A247006 1,1,1,3,9,45,225,1575,11025,99225,893025,9823275,108056025,
%T A247006 1404728325,18261468225,273922023375,4108832377650,69850150420050,
%U A247006 1187452281465450,22561593347843550,428670250038780750,9002075250814395750,189043575317350503750
%N A247006 Number of permutations on [n] admitting an eighth root.
%H A247006 Alois P. Heinz, <a href="/A247006/b247006.txt">Table of n, a(n) for n = 0..300</a>
%H A247006 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 A247006 with(combinat): with(numtheory): with(padic):
%p A247006 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
%p A247006       `if`(irem(j, mul(p^ordp(8, p), p=factorset(i)))=0, (i-1)!^j*
%p A247006       multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1), 0), j=0..n/i)))
%p A247006     end:
%p A247006 a:= n-> b(n$2):
%p A247006 seq(a(n), n=0..25);
%Y A247006 Column k=8 of A247005.
%K A247006 nonn
%O A247006 0,4
%A A247006 _Alois P. Heinz_, Sep 09 2014