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%I #7 Nov 04 2023 14:24:06
%S 1,2,6,21,91,385,1837,8272,39732,185592,891024,4183040,20199964,
%T 95232864,456282264,2162574984,10330196754,48834699384,232725598884,
%U 1098684561984,5214388065324,24591671545164,116257200312444,546797015443194,2578396047478494,12098087101521510
%N a(n) = Sum_{k=0..n} A000108(k) * A000041(k).
%F a(n) ~ 2^(2*n) * exp(Pi*sqrt(2*n/3)) / (3^(3/2) * sqrt(Pi) * n^(5/2)).
%t Table[Sum[CatalanNumber[k]*PartitionsP[k], {k, 0, n}], {n, 0, 30}]
%Y Cf. A000041, A000108, A356269, A367101.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Nov 04 2023