cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A087137 a(n) is the number of permutations in the symmetric group S_n that contain an odd cycle.

This page as a plain text file.
%I A087137 #14 Oct 18 2016 14:55:25
%S A087137 0,1,1,6,15,120,495,5040,29295,362880,2735775,39916800,370945575,
%T A087137 6227020800,68916822975,1307674368000,16813959537375,355687428096000,
%U A087137 5214921734397375,121645100408832000,2004231846526284375,51090942171709440000,934957186489800849375
%N A087137 a(n) is the number of permutations in the symmetric group S_n that contain an odd cycle.
%H A087137 Alois P. Heinz, <a href="/A087137/b087137.txt">Table of n, a(n) for n = 0..450</a>
%F A087137 E.g.f.: 1/(1-x)-1/sqrt(1-x^2).
%F A087137 If n is odd then a(n) = n! else a(n) = n!-((n-1)!!)^2.
%t A087137 CoefficientList[Series[1/(1-x)-1/Sqrt[1-x^2], {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Sep 21 2014 *)
%o A087137 (PARI) x='x+O('x^33); concat(0, Vec(serlaplace(1/(1-x)-1/sqrt(1-x^2)))) \\ _Michel Marcus_, Sep 21 2014
%Y A087137 Cf. A059838, A001818.
%K A087137 nonn
%O A087137 0,4
%A A087137 Yuval Dekel (dekelyuval(AT)hotmail.com), Oct 18 2003
%E A087137 Formulae and more terms from _Vladeta Jovovic_, Oct 31 2003
%E A087137 Two more terms from _Michel Marcus_, Sep 21 2014