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%I #6 Aug 01 2022 14:24:20
%S 1,3,9,49,189,945,4641,21801,99021,487981,2335541,10800725,51363065,
%T 238573865,1121139065,5309312105,24543884585,113220920945,
%U 530677144745,2439321389945,11261499234425,52169097691865,239433905462945,1095710701133345,5029918350471545
%N a(n) = Sum_{k=0..n} binomial(2*k, k) * q(k), where q(k) is the number of partitions into distinct parts (A000009).
%F a(n) ~ binomial(2*n,n) * q(n) * 4/3.
%F a(n) ~ 2^(2*n) * exp(Pi*sqrt(n/3)) / (3^(5/4) * sqrt(Pi) * n^(5/4)).
%t Table[Sum[Binomial[2*k, k] * PartitionsQ[k], {k, 0, n}], {n, 0, 30}]
%Y Cf. A000009, A006134, A032443, A266232, A307496, A356268, A356269.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Aug 01 2022