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A104625
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Expansion of 1/(sqrt(1-4*x) - x^2).
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3
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1, 2, 7, 24, 87, 322, 1211, 4604, 17645, 68042, 263655, 1025632, 4002601, 15662422, 61427543, 241386924, 950160607, 3745589510, 14784496003, 58424093536, 231112008371, 915065382154, 3626113490579, 14379912928572, 57064644495359
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OFFSET
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0,2
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COMMENTS
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Diagonal sums of convolution triangle of central binomial coefficients A054335.
Number of lattice paths from (0,0) to (n,n) with steps (0,1), (1,0) and, when on the diagonal, (2,2). - Alois P. Heinz, Sep 14 2016
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LINKS
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FORMULA
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Conjecture: n*a(n) + (n-3)*a(n-1) + 2*(-28*n+51)*a(n-2) + 72*(2*n-5)*a(n-3) - n*a(n-4) + (-5*n+3)*a(n-5) + 18*(2*n-5)*a(n-6) = 0. - R. J. Mathar, Feb 20 2015
a(n) = Sum_{k=0..floor(n+2)/2)} 4^(n+2-2*k) * binomial(n+1-3*k/2,n+2-2*k). - Seiichi Manyama, Feb 06 2024
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MATHEMATICA
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CoefficientList[Series[1/(Sqrt[1-4*x] -x^2), {x, 0, 50}], x] (* G. C. Greubel, Aug 12 2018 *)
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PROG
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(PARI) x='x+O('x^50); Vec(1/(sqrt(1-4*x) - x^2)) \\ G. C. Greubel, Aug 12 2018
(Magma) m:=50; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!(1/(sqrt(1-4*x) - x^2))); // G. C. Greubel, Aug 12 2018
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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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