A236357 E.g.f. satisfies: sin(x + A(x)) = A(x)^2.

-1, 2, -12, 120, -1680, 30360, -672000, 17599680, -532224000, 18248902560, -699544581120, 29645099003520, -1376154991411200, 69445751181206400, -3785191236642816000, 221613328121888102400, -13870531255760776396800, 924194452386724174656000

Offset: 1

Author

Vaclav Kotesovec, Jan 23 2014

Keywords

• sign

Comments

For n < 10 is |a(n)| = A215188(n), but a(10) is different.

Crossrefs

Cf. A215188, A143135.

Programs

Mathematica

Rest[CoefficientList[InverseSeries[Series[ArcSin[x^2]-x,{x,0,20}],x],x] * Range[0,20]!]

Formula

E.g.f.: Series_Reversion(arcsin(x^2)-x).

a(n) ~ (-1)^n * (4/sqrt(5)-8/5)^(1/4) * n^(n-1) / (exp(n) * (sqrt(sqrt(5)-2) - arcsin(sqrt(5)-2))^(n-1/2))