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%I #12 Jun 25 2022 01:32:51
%S 1,2,4,10,20,41,85,160,292,532,952,1624,2779,4597,7567,12319,19711,
%T 30997,48707,75167,115295,175487,264665,395185,587335,865371,1267311,
%U 1845231,2670627,3839267,5498051,7824331,11080441,15624505,21927225,30633780,42642416
%N a(n) = Sum_{k=0..n} p(k)*q(k), where p(k) = partition numbers (A000041) and q(k) = partition numbers into distinct parts (A000009).
%F a(n) ~ (sqrt(2)-1) * exp((1+sqrt(2))*Pi*sqrt(n/3)) / (8*3^(1/4)*Pi*n^(5/4)).
%t Table[Sum[PartitionsQ[k]*PartitionsP[k], {k,0,n}], {n,0,50}]
%Y Cf. A000009, A000041, A000070, A015128, A036469.
%Y Partial sums of A304991.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Dec 01 2015