%I #4 Jan 23 2014 08:23:46
%S -1,2,-12,120,-1680,30360,-672000,17599680,-532224000,18248902560,
%T -699544581120,29645099003520,-1376154991411200,69445751181206400,
%U -3785191236642816000,221613328121888102400,-13870531255760776396800,924194452386724174656000
%N E.g.f. satisfies: sin(x + A(x)) = A(x)^2.
%C For n < 10 is |a(n)| = A215188(n), but a(10) is different.
%F E.g.f.: Series_Reversion(arcsin(x^2)-x).
%F 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))
%t Rest[CoefficientList[InverseSeries[Series[ArcSin[x^2]-x,{x,0,20}],x],x] * Range[0,20]!]
%Y Cf. A215188, A143135.
%K sign
%O 1,2
%A _Vaclav Kotesovec_, Jan 23 2014
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