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%I #9 Aug 02 2022 05:51:06
%S 1,4,23,141,888,5675,36602,237563,1548995,10135554,66504699,437359454,
%T 2881641263,19016505326,125664684700,831400186740,5506287269802,
%U 36501297800013,242167539749593,1607851773270316,10682384379036741,71016046921543562,472376627798814453
%N a(n) = Sum_{k=0..n} binomial(3*n, n-k) * p(k), where p(k) is the partition function A000041.
%F a(n) ~ c * 3^(3*n + 1/2) / (sqrt(Pi*n) * 2^(2*n + 1)), where c = Sum_{j>=0} p(j)/2^j = A065446 = 3.4627466194550636115379573429...
%t Table[Sum[PartitionsP[k]*Binomial[3*n, n-k], {k, 0, n}], {n, 0, 30}]
%o (PARI) a(n) = sum(k=0, n, binomial(3*n, n-k)*numbpart(k)); \\ _Michel Marcus_, Aug 02 2022
%Y Cf. A000041, A188675, A356280, A356283.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Aug 01 2022