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%I #8 Sep 15 2021 10:25:35
%S 1,3,11,36,118,351,1082,3093,8984,25164,70434,191808,525559,1404672,
%T 3755506,9906111,26057062,67703310,175745506,451392114,1157272780,
%U 2944110060,7468477985,18821686554,47337840114,118344795738,295156919969,732694232394,1814357671094
%N a(n) = Sum_{k=0..n} 2^k * A000041(k) * A000009(n-k).
%F a(n) ~ A079555 * 2^n * A000041(n).
%F a(n) ~ QPochhammer(-1/2, 1/2) * 2^(n-2) * exp(Pi*sqrt(2*n/3)) / (sqrt(3)*n).
%F G.f.: Product_{k>=1} (1 + x^k) / (1 - 2^k*x^k).
%t Table[Sum[2^k*PartitionsP[k]*PartitionsQ[n-k], {k, 0, n}], {n, 0, 50}]
%t nmax = 50; CoefficientList[Series[Product[(1 + x^k) / (1 - 2^k*x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A000009, A000041, A015128, A079555, A264685, A347830.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Sep 15 2021