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%I #11 Jul 17 2017 02:53:53
%S 34459425,4583103525,353553700500,20941727706900,1063956789420525,
%T 49122916648430625,2133284602385096160,89095866141017736000,
%U 3632887356673057858375,146162134100332940264675,5846991791902793693661500,233881907399101905866222300
%N Number of permutations of [n] having exactly nine nontrivial cycles.
%C A nontrivial cycle has size > 1.
%H Alois P. Heinz, <a href="/A289957/b289957.txt">Table of n, a(n) for n = 18..450</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%F E.g.f.: (-log(1-x)-x)^9/9!*exp(x).
%t Drop[CoefficientList[Series[(-Log[1 - x] - x)^9/9!*Exp[x] , {x, 0, 50}], x] * Table[k !, {k, 0, 50}] , 18] (* _Indranil Ghosh_, Jul 16 2017 *)
%o (PARI) x = 'x + O('x^30); Vec(serlaplace((-log(1-x)-x)^9/9!*exp(x))) \\ _Michel Marcus_, Jul 16 2017
%Y Column k=9 of A136394.
%K nonn
%O 18,1
%A _Alois P. Heinz_, Jul 16 2017