A356282 a(n) = Sum_{k=0..n} binomial(3*n, n-k) * p(k), where p(k) is the partition function A000041.

1, 4, 23, 141, 888, 5675, 36602, 237563, 1548995, 10135554, 66504699, 437359454, 2881641263, 19016505326, 125664684700, 831400186740, 5506287269802, 36501297800013, 242167539749593, 1607851773270316, 10682384379036741, 71016046921543562, 472376627798814453

Offset: 0

Author

Vaclav Kotesovec, Aug 01 2022

Keywords

• nonn

Crossrefs

Cf. A000041, A188675, A356280, A356283.

Programs

Mathematica

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

PARI

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

Formula

a(n) ~ c * 3^(3*n + 1/2) / (sqrt(Pi*n) * 2^(2*n + 1)), where c = Sum_{j>=0} p(j)/2^j = A065446 = 3.4627466194550636115379573429...