A012629 Expansion of e.g.f. tanh(arcsinh(x)*arctan(x)) (only even powers).

0, 2, -12, -2, 10248, -914598, 58990140, 390971670, -1399074591600, 414051949573170, -75189740418805500, -1988456671385842770, 10786170755283590925720, -6649588570098570005749110, 2348244702630162770320062540, 166785234190504460598054627270, -1188356567924627353096569058456800

Offset

0,2

Links

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

Example

E.g.f. = 2/2!*x^2 - 12/4!*x^4 - 2/6!*x^6 + 10248/8!*x^8...

Mathematica

nmax=13; Join[{0}, DeleteElements[CoefficientList[Series[Tanh[ArcSinh[x]ArcTan[x]], {x, 0, 2*nmax}], x], {0}] (2Range[nmax])!] (* Stefano Spezia, Jan 24 2025 *)

Crossrefs

Cf. A012160, A012626.

Sequence in context: A185633 A246737 A012626 * A371589 A380389 A380390

Adjacent sequences: A012626 A012627 A012628 * A012630 A012631 A012632

Keyword

sign

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Extensions

Missing a(0) = 0 added by Stefano Spezia, Jan 24 2025

a(14)-a(16) from Stefano Spezia, Jan 25 2025

Status

approved