A013299 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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

LINKS

Table of n, a(n) for n=0..12.

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

Cf. A013302.

Sequence in context: A356505 A241999 A333005 * A013295 A214132 A196703

Adjacent sequences: A013296 A013297 A013298 * A013300 A013301 A013302

KEYWORD

nonn

AUTHOR

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

STATUS

approved