OFFSET
0,2
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
FORMULA
a(n) ~ (2*n)^(2*n+2)/exp(2*n). - Vaclav Kotesovec, Oct 24 2013
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Patrick Demichel (patrick.demichel(AT)hp.com)
STATUS
approved