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%I #10 Jul 24 2017 02:04:12
%S 10395,675675,26801775,855870015,24479795340,661680519500,
%T 17424049022380,455359195951660,11950227130952110,317363732767667950,
%U 8572733672197564870,236346930206430701350,6665648338618807806268,192596934884274256728700,5706700987506640526104700
%N Number of permutations of [n] having exactly six nontrivial cycles.
%C A nontrivial cycle has size > 1.
%H Alois P. Heinz, <a href="/A289954/b289954.txt">Table of n, a(n) for n = 12..450</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%F E.g.f.: (log(1-x)+x)^6/6!*exp(x).
%t Drop[Range[0, 30]! CoefficientList[Series[(Log[1 - x] + x)^6 / 6! Exp[x], {x, 0, 30}], x], 12] (* _Vincenzo Librandi_, Jul 24 2017 *)
%o (PARI) x = 'x + O('x^30); Vec(serlaplace((log(1-x)+x)^6/6!*exp(x))) \\ _Michel Marcus_, Jul 24 2017
%Y Column k=6 of A136394.
%K nonn
%O 12,1
%A _Alois P. Heinz_, Jul 16 2017
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