A012429 Expansion of e.g.f. cosh(arctan(x)*sin(x)) (only even powers).

1, 0, 12, -360, 17360, -1431360, 176717376, -30259605376, 6872523424000, -2001253898164224, 727157103049997312, -322526390192253356032, 171508583202445765136384, -107708920891668309118730240, 78871757493617689213300064256, -66610231446380635212936132526080, 64266796050146916106230446143111168

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 + 17360/8!*x^8 + ...

Mathematica

With[{nn=32}, Take[CoefficientList[Series[Cosh[ArcTan[x]Sin[x]], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Stefano Spezia, Dec 27 2025 *)

Crossrefs

Sequence in context: A009165 A012627 A012384 * A012631 A327986 A279182

Adjacent sequences: A012426 A012427 A012428 * A012430 A012431 A012432

Keyword

sign

Author

Patrick Demichel

Extensions

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

Status

approved