A013299 -sinh(log(x+1)-arctanh(x)) = 1/2!*x^2 + 6/4!*x^4 + 135/6!*x^6 + 6300/8!*x^8 + ...

1, 6, 135, 6300, 496125, 58939650, 9833098275, 2191376187000, 628651043645625, 225615874552818750, 99022807341232149375, 52176017395434685252500, 32501310835906189355203125

Offset: 0

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Keywords

• nonn

Comments

Number of degree-2n permutations without odd cycles and with odd number of even cycles, offset 1. E.g.f.: x^2/(2*sqrt(1-x^2)). - Vladeta Jovovic, Aug 10 2007

Crossrefs

Cf. A013302.

Programs

Mathematica

nn = 30; Select[Range[0, nn]! CoefficientList[Series[Sinh[Log[1/(1 - x^2)^(1/2)]], {x, 0, nn}], x], # > 0 &]  (* Geoffrey Critzer, Jan 15 2012 *)
With[{nn=30},Take[-CoefficientList[Series[Sinh[Log[x+1]-ArcTanh[x]], {x,0,nn}], x] Range[0,nn]!, {3,-1,2}]] (* Harvey P. Dale, Oct 30 2013 *)

Formula

a(n) ~ (2*n)^(2*n+2)/exp(2*n). - Vaclav Kotesovec, Oct 24 2013