A012632 Expansion of e.g.f. sec(arcsinh(x)*arctan(x)) (only even powers).

1, 0, 12, -360, 26768, -3003840, 500757312, -114797434752, 34719912016128, -13385737151096832, 6408112715151793152, -3729311544255904696320, 2592887206723575200256000, -2122643658026530680956928000, 2020918065940768920454195200000, -2214075437553357986660233703424000

Offset

0,3

Links

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

Example

E.g.f. = 1 + 12/4!*x^4 - 360/6!*x^6 + 26768/8!*x^8 + ...

Mathematica

With[{nn=30}, Take[CoefficientList[Series[Sec[ArcSinh[x]ArcTan[x]], {x, 0, nn}], x] Range[ 0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Nov 08 2022 *)

Crossrefs

Sequence in context: A393977 A012385 A012430 * A081791 A166183 A218310

Adjacent sequences: A012629 A012630 A012631 * A012633 A012634 A012635

Keyword

sign

Author

Patrick Demichel

Extensions

a(14)-a(15) from Stefano Spezia, Dec 27 2025

Status

approved