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 A356285 a(n) = Sum_{k=0..n} binomial(3*n, k) * q(k), where q(k) is the number of partitions into distinct parts (A000009). 1
 1, 4, 22, 214, 1509, 12770, 107884, 874365, 6834843, 56722759, 463069914, 3666488610, 29512199193, 233492075573, 1858649112464, 14890457067926, 117154630898329, 917101099859767, 7257072314543086, 56653800922475280, 442687465112658972, 3467083846726752495 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA a(n) ~ 3^(3*n + 1/4) * exp(Pi*sqrt(n/3)) / (sqrt(Pi) * n^(5/4) * 2^(2*n + 2)). MATHEMATICA Table[Sum[Binomial[3*n, k] * PartitionsQ[k], {k, 0, n}], {n, 0, 30}] CROSSREFS Cf. A000009, A188675, A356268, A356284. Sequence in context: A215201 A063380 A113385 * A120482 A207156 A197999 Adjacent sequences: A356282 A356283 A356284 * A356286 A356287 A356288 KEYWORD nonn AUTHOR Vaclav Kotesovec, Aug 01 2022 STATUS approved

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Last modified April 1 16:47 EDT 2023. Contains 361695 sequences. (Running on oeis4.)