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

0,3

Links

Table of n, a(n) for n=0..15.

Example

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

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 *)

Crossrefs

Sequence in context: A003749 A012395 A012687 * A009083 A012681 A009168

Adjacent sequences: A012464 A012465 A012466 * A012468 A012469 A012470

Keyword

sign

Author

Patrick Demichel

Extensions

Definition corrected by Harvey P. Dale, Apr 30 2012

Name edited by Jason Yuen, Aug 25 2025

Status

approved