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%I #8 Aug 27 2017 06:57:32
%S 0,0,0,0,2,5,11,22,40,70,116,187,292,448,670,988,1432,2051,2896,4052,
%T 5603,7687,10446,14096,18870,25108,33176,43601,56960,74051,95762,
%U 123300,158011,201692,256368,324682,409642,515116,645509,806430,1004292,1247146,1544237
%N Column 5 of A060244.
%H Vaclav Kotesovec, <a href="/A291590/b291590.txt">Table of n, a(n) for n = 1..10000</a>
%F G.f.: x^5 * (2 + 3*x + 2*x^2 + x^3 - 2*x^4 - 3*x^5 - 4*x^6 - 2*x^7 + 2*x^9 + 2*x^10 + x^11 - x^13)/((1 - x)^4 * (1 + x)^2 * (1 + x^2) * (1 + x + x^2) * (1 + x + x^2 + x^3 + x^4)) * Product_{k>=1} 1/(1 - x^k).
%F a(n) ~ sqrt(3) * n * exp(Pi*sqrt(2*n/3)) / (40*Pi^4).
%F a(n) ~ 3*n^2 * A000041(n) / (10*Pi^4).
%t nmax = 30; col = 5; Flatten[{0, 0, 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 Rest[CoefficientList[Series[x^5*(2 + 3*x + 2*x^2 + x^3 - 2*x^4 - 3*x^5 - 4*x^6 - 2*x^7 + 2*x^9 + 2*x^10 + x^11 - x^13)/((1 - x)^4 * (1 + x)^2 * (1 + x^2) * (1 + x + x^2) * (1 + x + x^2 + x^3 + x^4)) / QPochhammer[x], {x, 0, 100}], x]]
%t Table[Sum[(1 + (k-4)*(645 + 10*k + k^2)/720 - Floor[(k-4)/5]/5 - Floor[(k-4)/4]/4 + (k+1)*Floor[(k-4)/2]/8 - Floor[(k-3)/5]/5 - Floor[(k-3)/4]/4 - Floor[(k-3)/3]/3 - 3*Floor[(k-1)/5]/5) * PartitionsP[n-k], {k, 5, n}], {n, 1, 100}]
%Y Cf. A060244.
%K nonn
%O 1,5
%A _Vaclav Kotesovec_, Aug 27 2017
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