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A098337
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Expansion of 1/sqrt(1-4x+20x^2).
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3
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1, 2, -4, -40, -80, 352, 2624, 3712, -32000, -186880, -134144, 2885632, 13520896, -1269760, -256000000, -966164480, 1056112640, 22286827520, 66722201600, -162411315200, -1901125959680, -4329895362560
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OFFSET
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0,2
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COMMENTS
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Central coefficients of (1+2x-4x^2)^n. Binomial transform of A098334.
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LINKS
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FORMULA
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E.g.f.: exp(2x)BesselI(0, 4*I*x), I=sqrt(-1);
a(n) = sum{k=0..floor(n/2), binomial(n, k)binomial(n-k, k)2^n(-1)^k};
a(n) = sum{k=0..n, binomial(2k, k)binomial(k, n-k)(-5)^(n-k)}.
a(n) = Sum_{k=0..floor(n/2)} binomial(n, k)binomial(2(n-k), n)(-5)^k. - Paul Barry, Sep 08 2004.
D-finite with recurrence: n*a(n) +2*(-2*n+1)*a(n-1) +20*(n-1)*a(n-2)=0. - R. J. Mathar, Nov 24 2012
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MATHEMATICA
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Table[Sum[Binomial[n, k]*Binomial[2*(n-k), n]*(-5)^k, {k, 0, Floor[n/2]}], {n, 0, 20}] (* Vaclav Kotesovec, Feb 08 2014 *)
CoefficientList[Series[1/Sqrt[1-4x+20x^2], {x, 0, 30}], x] (* Harvey P. Dale, Jul 29 2015 *)
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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