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

1,2

Comments

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

Links

Table of n, a(n) for n=1..18.

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))

Mathematica

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

Crossrefs

Cf. A215188, A143135.

Sequence in context: A097388 A001813 A215188 * A226759 A303557 A131815

Adjacent sequences: A236354 A236355 A236356 * A236358 A236359 A236360

Keyword

sign

Author

Vaclav Kotesovec, Jan 23 2014

Status

approved