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A106184
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Expansion of 1/sqrt(1-4*x-8*x^2+32*x^3).
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2
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1, 2, 10, 28, 118, 380, 1508, 5240, 20326, 73836, 284396, 1061128, 4085820, 15500120, 59820040, 229366768, 887943046, 3428967500, 13315684764, 51678099304, 201246353492, 783890932488, 3060144292600, 11953056489104
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OFFSET
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0,2
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COMMENTS
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In general, a(n)=sum{k=0..floor(n/2), C(2k,k)C(2(n-2k),n-2k)*r^k} has g.f. 1/sqrt(1-4x-4r*x^2+16r*x^3).
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LINKS
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FORMULA
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a(n) = Sum_{k=0..floor(n/2)} C(2*k, k)*C(2(n-2*k), n-2*k)*2^k.
D-finite with recurrence: n*a(n)+2*(1-2*n)*a(n-1)+8*(1-n)*a(n-2)+16*(2*n-3)*a(n-3) = 0. - R. J. Mathar, Dec 08 2011
G.f. g(x) satisfies (4*x-1)*(8*x^2-1)*g'(x) + (48*x^2-8*x-2)*g(x) = 0, from which Mathar's recurrence can be derived. - Robert Israel, Feb 23 2016
a(n) = C(2*n,n)*hypergeom([1/2,-n/2,-n/2+1/2],[-n/2+3/4,-n/2+1/4],1/2). - Peter Luschny, Feb 23 2016
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MAPLE
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S:= series(1/sqrt(1-4*x-8*x^2+32*x^3), x, 101):
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MATHEMATICA
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CoefficientList[Series[1/Sqrt[1-4x-8x^2+32x^3], {x, 0, 30}], x] (* Harvey P. Dale, Sep 15 2011 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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