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G.f.: Sum_{k>=0} A000041(k)^2 * x^k / Sum_{k>=0} A000009(k) * x^k.
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%I #5 May 31 2018 02:47:30

%S 1,0,3,4,16,20,67,84,231,324,735,1026,2265,3086,6199,8880,16564,23390,

%T 42378,59496,103588,146376,244278,344186,564013,788168,1255201,

%U 1758400,2738833,3812242,5846114,8092092,12200957,16848156,24991705,34365176,50392543

%N G.f.: Sum_{k>=0} A000041(k)^2 * x^k / Sum_{k>=0} A000009(k) * x^k.

%F a(n) ~ 7^(3/2) * exp(Pi*sqrt(7*n/3)) / (768*n^2).

%t nmax = 50; CoefficientList[Series[Sum[PartitionsP[k]^2*x^k, {k, 0, nmax}] / Sum[PartitionsQ[k]*x^k, {k, 0, nmax}], {x, 0, nmax}], x]

%Y Cf. A000009, A000041, A001255, A054440, A304877, A305350.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, May 23 2018