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%I #16 Aug 27 2017 07:00:43
%S 0,0,1,2,4,8,13,22,35,54,81,121,174,250,352,491,675,924,1246,1674,
%T 2226,2944,3862,5046,6541,8449,10846,13869,17641,22365,28214,35485,
%U 44443,55494,69036,85650,105894,130594,160561,196923,240847,293907,357722,434477,526448
%N Column 3 of A060244.
%H Vaclav Kotesovec, <a href="/A291553/b291553.txt">Table of n, a(n) for n = 1..10000</a>
%F G.f.: x^3 * (1 + x - x^4) / ((1 - x)^2 * (1 + x) * (1 + x + x^2)) * Product_{k>=1} 1/(1 - x^k).
%F a(n) = Sum_{k=3..n} (floor(k/2) - floor((k-1)/3)) * A000041(n-k).
%F a(n) ~ exp(Pi*sqrt(2*n/3)) / (4*sqrt(3)*Pi^2).
%F a(n) ~ n * A000041(n) / Pi^2.
%t nmax = 50; col = 3; Flatten[{0, 0, CoefficientList[Coefficient[Normal[Series[Product[Product[1/(1 - x^(i - j)*y^j), {j, 0, i}], {i, 2, nmax + col}], {x, 0, col}, {y, 0, nmax}]], x^col], y]}]
%t nmax = 50; Rest[CoefficientList[Series[(x^3 * (1 + x - x^4))/((1-x)^2 * (1+x) * (1 + x + x^2)) / QPochhammer[x], {x, 0, nmax}], x]]
%t Table[Sum[(Floor[k/2] - Floor[(k-1)/3]) * PartitionsP[n-k], {k, 3, n}], {n, 1, 50}]
%Y Cf. A060244, A024786.
%K nonn
%O 1,4
%A _Vaclav Kotesovec_, Aug 26 2017
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