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A356281
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a(n) = Sum_{k=0..n} binomial(2*n, n-k) * q(k), where q(k) is the number of partitions into distinct parts (A000009).
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4
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1, 3, 11, 43, 172, 695, 2823, 11501, 46940, 191791, 784148, 3207196, 13119733, 53670793, 219545353, 897957702, 3672093558, 15013596535, 61370565546, 250803861369, 1024716136043, 4185683293934, 17093143284723, 69786349712519, 284847779542644, 1162385753008079
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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) ~ 2^(2*n - 1/2) * exp(3^(1/3) * Pi^(4/3) * n^(1/3) / 2^(8/3)) / sqrt(3*Pi*n).
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MATHEMATICA
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Table[Sum[PartitionsQ[k]*Binomial[2*n, n-k], {k, 0, n}], {n, 0, 30}]
nmax = 30; CoefficientList[Series[Sum[PartitionsQ[k]*((1-2*x-Sqrt[1-4*x])/(2*x))^k / Sqrt[1-4*x], {k, 0, nmax}], {x, 0, nmax}], x]
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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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