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A124213
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Expansion of e.g.f.: exp(exp(x)/sqrt(2-exp(2*x))-1).
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2
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1, 2, 12, 112, 1408, 22144, 417216, 9148416, 228649472, 6412193280, 199301663744, 6798026395648, 252397715738624, 10131114555244544, 437100940892913664, 20169428831476678656, 991081906535967948800, 51662621871173444698112, 2847287574653833612623872
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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E.g.f.: exp(exp(x)/sqrt(2-exp(2*x))-1).
a(n) ~ 2^(n + 1/6) * exp(3*n^(1/3)/(2^(2/3) * log(2)^(1/3)) - n - 1) * n^(n - 1/3) / (sqrt(3) * log(2)^(n + 1/6)). - Vaclav Kotesovec, Jun 26 2022
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MATHEMATICA
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With[{nmax = 50}, CoefficientList[Series[Exp[Exp[x]/Sqrt[2 - Exp[2*x]] - 1], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Sep 27 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(exp(exp(x)/sqrt(2-exp(2*x))-1))) \\ G. C. Greubel, Sep 27 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(Exp(x)/Sqrt(2-Exp(2*x))-1))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Sep 27 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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