A012627 Expansion of e.g.f. cos(arcsinh(x)*arctan(x)) (only even powers).

1, 0, -12, 360, -16688, 1189440, -122878272, 17448342912, -3261902393088, 775178137884672, -227406029305961472, 80264949964203755520, -33279338195895762923520, 15813964958377484261376000, -8361338503677113052655534080, 4703908965113942620906873651200, -2559171708261063456006373560483840

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 - 16688/8!*x^8 + ...

Mathematica

With[{nn=30}, Take[CoefficientList[Series[Cos[ArcSinh[x]ArcTan[x]], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Mar 27 2020 *)

Crossrefs

Sequence in context: A012379 A012424 A009165 * A012384 A012429 A012631

Adjacent sequences: A012624 A012625 A012626 * A012628 A012629 A012630

Keyword

sign

Author

Patrick Demichel

Extensions

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

Status

approved