A012633 Expansion of e.g.f. sech(arcsinh(x)*arctan(x)) (only even powers).

1, 0, -12, 360, -9968, -20160, 62513088, -11126763648, 1288066390272, 19652873951232, -83472832434404352, 36956701107235768320, -9713959158890293555200, -340935340396162516992000, 2635129523451479967361843200, -2149045686516779680223268864000, 953329799805918261075794900090880

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 - 9968/8!*x^8 + ...

Mathematica

With[{nn=30}, Take[CoefficientList[Series[Sech[ArcSinh[x]ArcTan[x]], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Jul 21 2018 *)

Crossrefs

Sequence in context: A012431 A012386 A130213 * A395124 A009079 A012379

Adjacent sequences: A012630 A012631 A012632 * A012634 A012635 A012636

Keyword

sign

Author

Patrick Demichel

Extensions

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

Status

approved