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A356285
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a(n) = Sum_{k=0..n} binomial(3*n, k) * q(k), where q(k) is the number of partitions into distinct parts (A000009).
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1
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1, 4, 22, 214, 1509, 12770, 107884, 874365, 6834843, 56722759, 463069914, 3666488610, 29512199193, 233492075573, 1858649112464, 14890457067926, 117154630898329, 917101099859767, 7257072314543086, 56653800922475280, 442687465112658972, 3467083846726752495
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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 + 1/4) * exp(Pi*sqrt(n/3)) / (sqrt(Pi) * n^(5/4) * 2^(2*n + 2)).
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MATHEMATICA
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Table[Sum[Binomial[3*n, k] * PartitionsQ[k], {k, 0, n}], {n, 0, 30}]
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CROSSREFS
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Cf. A000009, A188675, A356268, A356284.
Sequence in context: A215201 A063380 A113385 * A120482 A207156 A197999
Adjacent sequences: A356282 A356283 A356284 * A356286 A356287 A356288
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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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