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A113179
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Expansion of 1/sqrt((1-2x)^2-8x^3).
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2
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1, 2, 4, 12, 40, 128, 408, 1328, 4384, 14560, 48576, 162816, 547936, 1850048, 6263680, 21257856, 72298240, 246345728, 840775424, 2873802240, 9835840512, 33704557568, 115622041600, 397032488960, 1364610270720, 4694145256448
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OFFSET
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0,2
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COMMENTS
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In general, 1/sqrt((1-a*x)^2-4*b*x^3) expands to sum{k=0..floor(n/2), C(n-k,k)C(n-2k,k)b^k*a^(n-3k)}.
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LINKS
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FORMULA
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a(n)=sum{k=0..floor(n/2), C(n-k, k)C(n-2k, k)2^(n-2k)}.
D-finite with recurrence: n*a(n) +2*(-2*n+1)*a(n-1) +4*(n-1)*a(n-2) +4*(-2*n+3)*a(n-3)=0. [Belbachir]
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MATHEMATICA
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CoefficientList[Series[1/Sqrt[(1-2x)^2-8x^3], {x, 0, 30}], x] (* Harvey P. Dale, Dec 23 2017 *)
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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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