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
Keywords
Programs
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Mathematica
Table[Sum[Binomial[3*n, k] * PartitionsP[k], {k, 0, n}], {n, 0, 30}] -
PARI
a(n) = sum(k=0, n, binomial(3*n, k)*numbpart(k)); \\ Michel Marcus, Aug 02 2022
Formula
a(n) ~ 3^(3*n) * exp(Pi*sqrt(2*n/3)) / (sqrt(Pi) * n^(3/2) * 2^(2*n + 2)).