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A038602
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One half of convolution of central binomial coefficients A000984(n) with A000984(n+2), n >= 0.
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1
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3, 16, 73, 316, 1334, 5552, 22901, 93892, 383290, 1559680, 6331098, 25649976, 103758828, 419195552, 1691825933, 6822051092, 27488564498, 110691186272, 445487285678, 1792047789512, 7205785665908, 28963557761312
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OFFSET
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0,1
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COMMENTS
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Also convolution of A000346 with Catalan numbers but with C(0)=1 replaced by 3
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LINKS
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FORMULA
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a(n) = 2^(2*n+3)-(3*n+5)*C(n+1), C(n): Catalan numbers A000108.
G.f.: c(x)*(c(x)+2)/(1-4*x), where c(x) is G.f. for Catalan numbers.
Recurrence: n*(n+2)*a(n) = 2*(4*n^2 + 5*n - 1)*a(n-1) - 8*(n+1)*(2*n-1)*a(n-2). - Vaclav Kotesovec, Mar 28 2014
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MATHEMATICA
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CoefficientList[Series[(1-Sqrt[1-4*x])/(2*x)*((1-Sqrt[1-4*x])/(2*x)+2)/(1-4*x), {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 28 2014 *)
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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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