A012344 cos(arcsin(x)*arcsin(x))=1-12/4!*x^4-240/6!*x^6-7728/8!*x^8...

1, 0, -12, -240, -7728, -428160, -37912512, -4960720128, -901797013248, -217415865765888, -67097095431416832, -25783170924788428800, -12066773451365568000000, -6755136268249010663424000

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..224

Formula

a(n) ~ -sqrt(Pi) * sin(Pi^2/4) * (2*n)! / (2 * n^(3/2)). - Vaclav Kotesovec, Feb 08 2015

Example

cos(arcsin(x)*arcsin(x)) = 1 - 12/4!*x^4 - 240/6!*x^6 - 7728/8!*x^8 + ...

Mathematica

nn = 20; Table[(CoefficientList[Series[Cos[ArcSin[x]^2], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Feb 08 2015 *)

Prog

(PARI) x='x+O('x^50); v=Vec(serlaplace(cos(asin(x)*asin(x)))); vector(#v\2, n, v[2*n-1]) \\ G. C. Greubel, Apr 11 2017

Crossrefs

Sequence in context: A034910 A332958 A091745 * A282789 A012542 A009166

Adjacent sequences: A012341 A012342 A012343 * A012345 A012346 A012347

Keyword

sign

Author

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

Status

approved