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%I #6 May 23 2023 15:12:16
%S 1,1,2,6,10,21,44,75,132,240,420,672,1155,1818,2970,4752,7392,11286,
%T 17710,26460,40128,60192,89178,130520,192150,278036,401940,577920,
%U 825396,1168640,1658784,2326280,3256110,4544064,6302720,8706555,12008636,16444120,22476960
%N a(n) = A000041(n) * A000009(n).
%F a(n) ~ exp(Pi*(1+sqrt(2))*sqrt(n/3)) / (16*3^(3/4)*n^(7/4)).
%p b:= proc(n) option remember; `if`(n=0, 1, add(b(n-j)*add(
%p `if`(d::odd, d, 0), d=numtheory[divisors](j)), j=1..n)/n)
%p end:
%p a:= n-> b(n)*combinat[numbpart](n):
%p seq(a(n), n=0..40); # _Alois P. Heinz_, May 23 2023
%t Table[PartitionsP[n]*PartitionsQ[n], {n, 0, 50}]
%Y Cf. A000009, A000041, A015128.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, May 23 2018
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