A356283 a(n) = Sum_{k=0..n} binomial(3*n, n-k) * q(k), where q(k) is the number of partitions into distinct parts (A000009).

1, 4, 22, 131, 807, 5066, 32188, 206242, 1329733, 8614685, 56024538, 365491218, 2390613557, 15671221522, 102925324569, 677110860689, 4460956827127, 29427611146335, 194348311824025, 1284856925961827, 8502252246841668, 56309476194587377, 373220349572126265

Offset: 0

Author

Vaclav Kotesovec, Aug 01 2022

Keywords

• nonn

Crossrefs

Cf. A000009, A188675, A356281, A356282.

Programs

Mathematica

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

Formula

a(n) ~ c * 3^(3*n + 1/2) / (sqrt(Pi*n) * 2^(2*n + 1)), where c = Sum_{j>=0} q(j)/2^j = A079555 = 2.384231029031371724149899288678...