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A081922
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Expansion of exp(4x)/sqrt(1-x^2).
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1
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1, 4, 17, 76, 361, 1844, 10321, 64348, 453329, 3619684, 32666161, 329434604, 3677682937, 44901581716, 595567550321, 8505627039484, 130307878338721, 2126927187154628, 36912563369550289, 677277819029706124
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OFFSET
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0,2
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COMMENTS
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Generally, if e.g.f. = exp(p*x)/sqrt(1-x^2), then a(n) ~ n^n * (exp(p)+(-1)^n*exp(-p)) / exp(n). - Vaclav Kotesovec, Feb 04 2014
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LINKS
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FORMULA
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E.g.f.: exp(4x)/sqrt(1-x^2).
D-finite with recurrence: -a(n) + 4*a(n-1) + (n-1)^2*a(n-2) - 4*(n-1)*(n-2)*a(n-3) = 0. - R. J. Mathar, Nov 09 2012
a(n) ~ n^n * (exp(4) + (-1)^n*exp(-4)) / exp(n). - Vaclav Kotesovec, Feb 04 2014
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[Exp[4x]/Sqrt[1-x^2] , {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, May 07 2012 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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