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A281809 Expansion of Sum_{i>=1} x^(i^3) / (1 - Sum_{j>=1} x^(j^3))^2.

%I A281809 #7 Aug 07 2019 18:01:49
%S A281809 1,2,3,4,5,6,7,9,13,19,27,37,49,63,79,99,126,163,213,279,364,471,603,
%T A281809 766,970,1229,1562,1992,2545,3251,4144,5266,6672,8435,10655,13462,
%U A281809 17019,21527,27230,34425,43478,54846,69114,87032,109555,137889,173543,218393,274765,345544,434332,545650,685187,860105,1079402
%N A281809 Expansion of Sum_{i>=1} x^(i^3) / (1 - Sum_{j>=1} x^(j^3))^2.
%C A281809 Total number of parts in all compositions (ordered partitions) of n into cubes (A000578).
%H A281809 Alois P. Heinz, <a href="/A281809/b281809.txt">Table of n, a(n) for n = 1..10919</a>
%H A281809 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%H A281809 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A281809 G.f.: Sum_{i>=1} x^(i^3) / (1 - Sum_{j>=1} x^(j^3))^2.
%e A281809 a(10) = 19 because we have [8, 1, 1], [1, 8, 1], [1, 1, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] and 3 + 3 + 3 + 10 = 19.
%p A281809 b:= proc(n) option remember; `if`(n=0, [1, 0], add(
%p A281809       (p-> p+[0, p[1]])(b(n-j^3)), j=1..iroot(n, 3)))
%p A281809     end:
%p A281809 a:= n-> b(n)[2]:
%p A281809 seq(a(n), n=1..55);  # _Alois P. Heinz_, Aug 07 2019
%t A281809 nmax = 55; Rest[CoefficientList[Series[Sum[x^i^3, {i, 1, nmax}]/(1 - Sum[x^j^3, {j, 1, nmax}])^2, {x, 0, nmax}], x]]
%Y A281809 Cf. A000578, A023358.
%K A281809 nonn
%O A281809 1,2
%A A281809 _Ilya Gutkovskiy_, Jan 30 2017