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G.f.: Product_{k>=1, j>=1} 1/(1 - x^(j*k^3)).
3

%I #6 Jan 07 2017 06:39:48

%S 1,1,2,3,5,7,11,15,23,31,44,59,82,108,146,191,255,329,431,552,714,907,

%T 1159,1461,1853,2318,2911,3622,4515,5582,6912,8499,10464,12801,15667,

%U 19079,23236,28168,34142,41222,49755,59836,71926,86190,103218,123262,147091

%N G.f.: Product_{k>=1, j>=1} 1/(1 - x^(j*k^3)).

%H Vaclav Kotesovec, <a href="/A280661/b280661.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ exp(Pi*sqrt(2*Zeta(3)*n/3) + Pi^(-1/3) * Gamma(4/3) * Zeta(4/3) * Zeta(1/3) * (6*n/Zeta(3))^(1/6)) * Pi^(3/4) * Zeta(3)^(1/8) / (6^(1/8) * n^(5/8)).

%t nmax = 100; CoefficientList[Series[1/Product[1-x^(j*k^3), {k, 1, Floor[nmax^(1/3)]+1}, {j, 1, Floor[nmax/k^3]+1}], {x, 0, nmax}], x]

%Y Cf. A006171, A004101, A280662.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Jan 07 2017