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A356286
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a(n) = Sum_{k=0..n} binomial(3*k, k) * p(k), where p(k) is the partition function A000041.
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1
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1, 4, 34, 286, 2761, 23782, 227986, 1972186, 18152548, 158757298, 1420647928, 12258704248, 108637887148, 929002856992, 8065133782792, 68761800685576, 589631899738033, 4976639418495358, 42293283621258283, 354415428588891283, 2982701933728936648, 24857294772400460368
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..21.
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FORMULA
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a(n) ~ 3^(3*n+3) * exp(Pi*sqrt(2*n/3)) / (23 * sqrt(Pi) * n^(3/2) * 2^(2*n+3)).
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MATHEMATICA
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Table[Sum[Binomial[3*k, k] * PartitionsP[k], {k, 0, n}], {n, 0, 30}]
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PROG
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(PARI) a(n) = sum(k=0, n, binomial(3*k, k)*numbpart(k)); \\ Michel Marcus, Aug 02 2022
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CROSSREFS
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Cf. A000041, A188675, A356269, A356287.
Sequence in context: A201684 A155628 A346936 * A036352 A005569 A232910
Adjacent sequences: A356283 A356284 A356285 * A356287 A356288 A356289
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KEYWORD
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nonn
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AUTHOR
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Vaclav Kotesovec, Aug 01 2022
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STATUS
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approved
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