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%I #6 Nov 04 2023 14:23:31
%S 1,2,4,14,42,168,696,2841,11421,50317,218277,923709,4043889,17416089,
%T 76253769,338014584,1469460024,6395962044,28367342244,123799554504,
%U 543903261384,2403339554904,10545287718864,46223487538464,203591793511992,893988182518176,3924601439423256
%N a(n) = Sum_{k=0..n} A000108(k) * A000009(k).
%F a(n) ~ 2^(2*n) * exp(Pi*sqrt(n/3)) / (3^(5/4) * sqrt(Pi) * n^(9/4)).
%t Table[Sum[CatalanNumber[k]*PartitionsQ[k], {k, 0, n}], {n, 0, 30}]
%Y Cf. A000009, A000108, A356270, A367100.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Nov 04 2023