A356286 - OEIS

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

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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