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A137635
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a(n) = Sum_{k=0..n} C(2k,k)*C(2k,n-k); equals row 0 of square array A137634.
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20
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1, 2, 10, 46, 226, 1136, 5810, 30080, 157162, 826992, 4376408, 23267332, 124179570, 664919780, 3570265000, 19216805476, 103652442922, 560127574340, 3031887311256, 16435458039076, 89213101943000, 484839755040768, 2637805800869740, 14365506336197816
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OFFSET
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0,2
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COMMENTS
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Diagonal of rational function 1/(1 - (x + y + x^2*y + x*y^2)). - Gheorghe Coserea, Aug 31 2018
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LINKS
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FORMULA
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G.f.: A(x) = 1/sqrt(1 - 4x(1+x)^2).
D-finite with recurrence: n*a(n) +2*(-2*n+1)*a(n-1) +8*(-n+1)*a(n-2) +2*(-2*n+3)*a(n-3)=0. - R. J. Mathar, Jan 14 2020
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MATHEMATICA
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CoefficientList[Series[1/Sqrt[1 - 4*x*(1 + x)^2], {x, 0, 50}], x] (* Stefano Spezia, Sep 01 2018 *)
Table[Sum[Binomial[2k, k]Binomial[2k, n-k], {k, 0, n}], {n, 0, 30}] (* Harvey P. Dale, Dec 31 2018 *)
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PROG
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(PARI) a(n)=sum(k=0, n, binomial(2*k, k)*binomial(2*k, n-k));
(PARI) a(n)=polcoeff(1/sqrt(1-4*x*(1+x +x*O(x^n))^2), n, x); /* Using the g.f.: */
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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