A356287 a(n) = Sum_{k=0..n} binomial(3*k, k) * q(k), where q(k) is the number of partitions into distinct parts (A000009).
1, 4, 19, 187, 1177, 10186, 84442, 665842, 5078668, 42573268, 343023418, 2665464058, 21440629558, 167644287550, 1330569327310, 10641989818078, 82797155054782, 644097780350332, 5102709814966162, 39499844158337962, 307777892529889642, 2406854983109480302
Offset: 0
Keywords
Programs
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Mathematica
Table[Sum[Binomial[3*k, k] * PartitionsQ[k], {k, 0, n}], {n, 0, 30}]
Formula
a(n) ~ 3^(3*n + 13/4) * exp(Pi*sqrt(n/3)) / (23 * sqrt(Pi) * n^(5/4) * 2^(2*n+3)).