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a(n) = [x^(n^3)] (1/(1 - x))*(Sum_{k>=1} x^(k^3))^n.
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%I #5 Apr 28 2018 17:16:44

%S 1,1,1,8,66,512,5269,57459,711742,9610222,139735699,2183555015,

%T 36543300668,649320343729,12174674648730,240360451018461,

%U 4975239937954534,107600744797471150,2426579187889852885,56901290353169050995,1384258146777832889697

%N a(n) = [x^(n^3)] (1/(1 - x))*(Sum_{k>=1} x^(k^3))^n.

%C Number of positive solutions to (x_1)^3 + (x_2)^3 + ... + (x_n)^3 <= n^3.

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>

%t Join[{1}, Table[SeriesCoefficient[1/(1 - x) Sum[x^k^3, {k, 1, n}]^n, {x, 0, n^3}], {n, 20}]]

%Y Cf. A000578, A010057, A051344, A280618, A298672, A302995, A303169.

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Apr 24 2018