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

%I

%S 1,2,20,488,22416,1680672,187766592,29343408768,6124074217728,

%T 1647634955248128,555774895924564992,229837057464353187840,

%U 114397631096541960376320,67482635629160164765409280

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

%H G. C. Greubel, <a href="/A012340/b012340.txt">Table of n, a(n) for n = 0..220</a>

%F a(n) ~ exp(Pi^2/4) * sqrt(Pi) * (2*n-1)! / sqrt(n). - _Vaclav Kotesovec_, Feb 08 2015

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

%t 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 *)

%o (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

%K nonn

%O 0,2

%A Patrick Demichel (patrick.demichel(AT)hp.com)

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Last modified February 5 12:47 EST 2023. Contains 360084 sequences. (Running on oeis4.)