A356287 a(n) = Sum_{k=0..n} binomial(3*k, k) * q(k), where q(k) is the number of partitions into distinct parts (A000009).

1, 4, 19, 187, 1177, 10186, 84442, 665842, 5078668, 42573268, 343023418, 2665464058, 21440629558, 167644287550, 1330569327310, 10641989818078, 82797155054782, 644097780350332, 5102709814966162, 39499844158337962, 307777892529889642, 2406854983109480302

Offset

0,2

Links

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

Formula

a(n) ~ 3^(3*n + 13/4) * exp(Pi*sqrt(n/3)) / (23 * sqrt(Pi) * n^(5/4) * 2^(2*n+3)).

Mathematica

Table[Sum[Binomial[3*k, k] * PartitionsQ[k], {k, 0, n}], {n, 0, 30}]

Crossrefs

Cf. A000009, A188675, A356270, A356286.

Sequence in context: A292167 A126147 A007411 * A377004 A276259 A072879

Adjacent sequences: A356284 A356285 A356286 * A356288 A356289 A356290

Keyword

nonn

Author

Vaclav Kotesovec, Aug 01 2022

Status

approved