A012340 exp(arcsin(x)*arcsin(x))=1+2/2!*x^2+20/4!*x^4+488/6!*x^6+22416/8!*x^8...

1, 2, 20, 488, 22416, 1680672, 187766592, 29343408768, 6124074217728, 1647634955248128, 555774895924564992, 229837057464353187840, 114397631096541960376320, 67482635629160164765409280

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..220

Formula

a(n) ~ exp(Pi^2/4) * sqrt(Pi) * (2*n-1)! / sqrt(n). - Vaclav Kotesovec, Feb 08 2015

Example

exp(arcsin(x)*arcsin(x)) = 1 + 2/2!*x^2 + 20/4!*x^4 + 488/6!*x^6 + 22416/8!*x^8 + ...

Mathematica

nn = 20; Table[(CoefficientList[Series[E^(ArcSin[x]^2), {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Feb 08 2015 *)
With[{nn=30}, Take[CoefficientList[Series[Exp[ArcSin[x]^2], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Nov 23 2024 *)

Prog

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

Crossrefs

Sequence in context: A274738 A352250 A012816 * A279839 A279837 A279200

Adjacent sequences: A012337 A012338 A012339 * A012341 A012342 A012343

Keyword

nonn

Author

Patrick Demichel

Status

approved