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

0,2

Links

Table of n, a(n) for n=0..22.

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...

Mathematica

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

Prog

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

Crossrefs

Cf. A000041, A188675, A356280, A356283.

Sequence in context: A067110 A290052 A158197 * A038736 A091642 A162561

Adjacent sequences: A356279 A356280 A356281 * A356283 A356284 A356285

Keyword

nonn

Author

Vaclav Kotesovec, Aug 01 2022

Status

approved