A289956 - OEIS

A289956

Number of permutations of [n] having exactly eight nontrivial cycles.

%I #11 Jul 17 2017 02:53:43

%S 2027025,218243025,13818229425,680438103345,29079209884725,

%T 1141483113695925,42556765607801445,1539279211706361125,

%U 54789078082648965055,1938102614993339970175,68612592434209034386175,2443274471026078967051775,87839862102761225799417075

%N Number of permutations of [n] having exactly eight nontrivial cycles.

%C A nontrivial cycle has size > 1.

%H Alois P. Heinz, <a href="/A289956/b289956.txt">Table of n, a(n) for n = 16..450</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>

%F E.g.f.: (log(1-x)+x)^8/8!*exp(x).

%t Drop[CoefficientList[Series[(Log[1 - x] + x)^8/8!*Exp[x] , {x, 0, 50}], x] * Table[k !, {k, 0, 50}] , 16] (* _Indranil Ghosh_, Jul 16 2017 *)

%o (PARI) x = 'x + O('x^30); Vec(serlaplace((-log(1-x)-x)^8/8!*exp(x))) \\ _Michel Marcus_, Jul 16 2017

%Y Column k=8 of A136394.

%K nonn

%O 16,1

%A _Alois P. Heinz_, Jul 16 2017