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A243204
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Expansion of 2*x/((1-sqrt(1-2*(1-sqrt(1-4*x))))*sqrt(1-2*(1-sqrt(1-4*x))) * sqrt(1-4*x)).
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1
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1, 2, 8, 35, 160, 752, 3605, 17544, 86400, 429605, 2153008, 10860720, 55086421, 280692440, 1435868960, 7369703660, 37934443008, 195748568256, 1012292239955, 5244933087000, 27220980100160, 141486701601630
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} binomial(2*k-1,k)*binomial(2*n-k-1,n-k)).
G.f.: A(x) = x*F'(x)/F(x), where F(x)=x*C(x)*C(x*C(x)), C(x) is g.f. of A000108.
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MATHEMATICA
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CoefficientList[Series[2*x / (Sqrt[1-4*x] + Sqrt[-1+2*Sqrt[1-4*x]] *Sqrt[1-4*x] + 8*x-2), {x, 0, 20}], x] (* Vaclav Kotesovec, Jun 02 2014 *)
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PROG
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(Maxima)
a(n):=sum(binomial(2*k-1, k)*binomial(2*n-k-1, n-k), k, 0, n);
(PARI) x='x+O('x^50); Vec(2*x/((1-sqrt(1-2*(1-sqrt(1-4*x))))*sqrt(1-2*(1-sqrt(1-4*x)))*sqrt(1-4*x))) \\ G. C. Greubel, Jun 01 2017
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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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