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A296464 Expansion of e.g.f. arcsin(arcsin(x)) (odd powers only). 7

%I

%S 1,2,28,1024,71632,8192736,1392793920,330041217024,104069101383936,

%T 42159457593506304,21346870862961183744,13213529766600134344704,

%U 9818417126704155249954816,8625630408510010165396070400,8844234850947343105068735283200,10467364426053362392901751845683200

%N Expansion of e.g.f. arcsin(arcsin(x)) (odd powers only).

%F E.g.f.: arcsinh(arcsinh(x)) (odd powers only, absolute values).

%F E.g.f.: -i*log(log(i*x + sqrt(1 - x^2)) + sqrt(1 + log(i*x + sqrt(1 - x^2))^2)), where i is the imaginary unit (odd powers only).

%F a(n) ~ sqrt(2) * (2*n)! / (sqrt(Pi*sin(2)*n) * sin(1)^(2*n)). - _Vaclav Kotesovec_, Dec 13 2017

%e arcsin(arcsin(x)) = x/1! + 2*x^3/3! + 28*x^5/5! + 1024*x^7/7! + 71632*x^9/9! + ...

%t nmax = 16; Table[(CoefficientList[Series[ArcSin[ArcSin[x]], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]

%t nmax = 16; Table[(CoefficientList[Series[-I Log[Log[I x + Sqrt[1 - x^2]] + Sqrt[1 + Log[I x + Sqrt[1 - x^2]]^2]], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]

%Y Cf. A001818, A003712, A012063, A296466.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Dec 13 2017

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Last modified September 22 00:42 EDT 2020. Contains 337276 sequences. (Running on oeis4.)