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%I #15 Jun 24 2022 20:12:56
%S 0,1,3,9,17,32,56,91,139,211,311,443,623,857,1165,1570,2082,2728,3556,
%T 4582,5862,7458,9416,11808,14736,18286,22576,27760,33976,41400,50280,
%U 60820,73300,88084,105492,125967,150015,178135,210967,249265,293785,345445,405337
%N a(n) = Sum_{k=0..n} k*A000009(k).
%F a(n) ~ 3^(1/4) * n^(3/4) * exp(sqrt(n/3)*Pi) / (2*Pi).
%F G.f.: x*f'(x)/(1 - x), where f(x) = Product_{k>=1} (1 + x^k). - _Ilya Gutkovskiy_, Apr 13 2017
%t Table[Sum[PartitionsQ[k]*k, {k, 0, n}], {n, 0, 50}]
%Y Cf. A000009, A000070, A014153, A036469, A095944, A182738.
%Y Partial sums of A066189.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Mar 12 2016
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