A356284 a(n) = Sum_{k=0..n} binomial(3*n, k) * p(k), where p(k) is the partition function A000041.

1, 4, 37, 334, 3280, 29437, 282253, 2517904, 23209785, 206685325, 1858085653, 16266231810, 144339750406, 1250038867329, 10882952174845, 93546973843450, 804847296088574, 6843680884286307, 58300294406199829, 491683063753997014, 4148296662116385627, 34746182976196757434

Offset

0,2

Links

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

Formula

a(n) ~ 3^(3*n) * exp(Pi*sqrt(2*n/3)) / (sqrt(Pi) * n^(3/2) * 2^(2*n + 2)).

Mathematica

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

Prog

(PARI) a(n) = sum(k=0, n, binomial(3*n, k)*numbpart(k)); \\ Michel Marcus, Aug 02 2022

Crossrefs

Cf. A000041, A188675, A356267, A356285.

Sequence in context: A025542 A162649 A221059 * A197966 A199690 A133462

Adjacent sequences: A356281 A356282 A356283 * A356285 A356286 A356287

Keyword

nonn

Author

Vaclav Kotesovec, Aug 01 2022

Status

approved