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, 4, 22, 214, 1509, 12770, 107884, 874365, 6834843, 56722759, 463069914, 3666488610, 29512199193, 233492075573, 1858649112464, 14890457067926, 117154630898329, 917101099859767, 7257072314543086, 56653800922475280, 442687465112658972, 3467083846726752495

Offset

0,2

Links

Table of n, a(n) for n=0..21.

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