A356290 a(n) = Sum_{k=0..n} binomial(3*n, n-k) * v(k), where v(k) is the number of overpartitions of n (A015128).

1, 5, 31, 200, 1309, 8627, 57082, 378648, 2516111, 16740913, 111494801, 743137984, 4956359312, 33074272702, 220810039566, 1474764797488, 9853307017341, 65853733243281, 440255398634199, 2944041287677060, 19691951641479427, 131744163990056479, 881586559906575688

Offset: 0

Author

Vaclav Kotesovec, Aug 02 2022

Keywords

• nonn

Crossrefs

Cf. A015128, A266497, A356280, A356281, A356282, A356283, A356289.

Programs

Mathematica

Table[Sum[Sum[PartitionsP[k-j]*PartitionsQ[j], {j, 0, 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} v(j)/2^j = 8.2559879357782500655441408494322731265270016167882303456037...