A012467 Expansion of e.g.f. sech(arctan(x)^2), even powers only.

1, 0, -12, 480, -21168, 741120, 61942848, -29951061504, 8015861467392, -1745546459848704, 215844160641143808, 91751419512905687040, -109687232118939992862720, 71900040403600384794624000, -32879657977585141660017868800, 2569990403264790442179575808000

Offset: 0

Author

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

Keywords

• sign
• changed

Examples

			1 - 12/4!*x^4 + 480/6!*x^6 - 21168/8!*x^8 + ...
		

Programs

Mathematica

With[{nn=30},Take[CoefficientList[Series[Sech[ArcTan[x]^2],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* Harvey P. Dale, Apr 30 2012 *)

Extensions

Definition corrected by Harvey P. Dale, Apr 30 2012

Name edited by Jason Yuen, Aug 25 2025