A012424 Expansion of e.g.f. cos(arctan(x)*sin(x)) (only even powers).

1, 0, -12, 360, -14000, 826560, -74707776, 9918004096, -1826276458240, 443565659817984, -136830226103770112, 52123659256392435712, -23992831220659002945536, 13113491065080505366691840, -8387303391984941706785734656, 6200299131133980707312718151680, -5241128596539643450355248900538368

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 - 14000/8!*x^8 + ...

Mathematica

With[{nn=30}, Take[CoefficientList[Series[Cos[ArcTan[x]Sin[x]], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, May 24 2015 *)

Crossrefs

Sequence in context: A395124 A009079 A012379 * A009165 A012627 A012384

Adjacent sequences: A012421 A012422 A012423 * A012425 A012426 A012427

Keyword

sign

Author

Patrick Demichel

Extensions

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

Status

approved