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%I #5 Aug 02 2022 06:40:22
%S 1,4,18,82,372,1676,7500,33358,147570,649722,2848524,12441434,
%T 54155774,235008672,1016971480,4389589484,18902538548,81222609020,
%U 348308661820,1490884718484,6370468593732,27176620756392,115760526170340,492386739902574,2091554077819948,8873225318953248
%N a(n) = Sum_{k=0..n} binomial(2*n, n-k) * v(k), where v(k) is the number of overpartitions of n (A015128).
%F a(n) ~ 2^(2*n - 7/6) * exp(3 * Pi^(4/3) * n^(1/3) / 2^(8/3)) / (sqrt(3) * Pi^(2/3) * n^(2/3)).
%t Table[Sum[Sum[PartitionsP[k-j]*PartitionsQ[j], {j, 0, k}] * Binomial[2*n, n-k], {k, 0, n}], {n, 0, 30}]
%Y Cf. A015128, A266497, A356280, A356281, A356282, A356283, A356290.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Aug 02 2022
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