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

%I #5 Jan 07 2017 06:39:19

%S 1,1,1,2,2,3,4,5,7,9,11,14,17,21,26,32,39,47,57,68,81,97,115,136,162,

%T 190,223,263,306,357,417,483,561,650,750,866,997,1145,1315,1507,1725,

%U 1971,2250,2564,2917,3318,3766,4270,4840,5475,6188,6990,7881,8881

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

%H Vaclav Kotesovec, <a href="/A280663/b280663.txt">Table of n, a(n) for n = 0..10000</a>

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

%t nmax = 100; CoefficientList[Series[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. A107742, A280451, A280664.

%K nonn

%O 0,4

%A _Vaclav Kotesovec_, Jan 07 2017