A012431 Expansion of e.g.f. sech(arctan(x)*sin(x)) (only even powers).

1, 0, -12, 360, -7280, -383040, 89394624, -8970625664, -316692862720, 470941672802304, -146844936720038912, 18279034160407939072, 9932590980055055503360, -8395139128320596309032960, 2335687341411368705089388544, 1712350162842269820444558458880, -3058689468808989441858872938528768

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Example

E.g.f. = 1 - 12/4!*x^4 + 360/6!*x^6 - 7280/8!*x^8 + ...

Mathematica

With[{nn=30}, Take[CoefficientList[Series[Sech[ArcTan[x]Sin[x]], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Aug 28 2017 *)

Crossrefs

Sequence in context: A074094 A012553 A128043 * A012386 A130213 A012633

Adjacent sequences: A012428 A012429 A012430 * A012432 A012433 A012434

Keyword

sign

Author

Patrick Demichel

Extensions

a(14)-a(16) from Stefano Spezia, Dec 27 2025

Status

approved