A356286 a(n) = Sum_{k=0..n} binomial(3*k, k) * p(k), where p(k) is the partition function A000041.

1, 4, 34, 286, 2761, 23782, 227986, 1972186, 18152548, 158757298, 1420647928, 12258704248, 108637887148, 929002856992, 8065133782792, 68761800685576, 589631899738033, 4976639418495358, 42293283621258283, 354415428588891283, 2982701933728936648, 24857294772400460368

Offset

0,2

Links

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000041, A188675, A356269, A356287.

Sequence in context: A201684 A155628 A346936 * A036352 A005569 A370171

Adjacent sequences: A356283 A356284 A356285 * A356287 A356288 A356289

Keyword

nonn

Author

Vaclav Kotesovec, Aug 01 2022

Status

approved