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%I #7 Apr 05 2017 04:47:25
%S 1,2,3,5,6,7,8,11,13,14,15,19,21,22,23,29,31,34,35,42,44,47,48,56,60,
%T 63,67,76,80,83,87,99,103,108,112,130,134,139,143,162,169,174,180,200,
%U 213,218,224,248,262,272,278,306,320,337,343,372,390,408,419,449,471,489,508,544,567,591,611,654,677,705
%N Expansion of Sum_{i>=1} x^(i^2)/(1 - x^(i^2)) * Product_{j=1..i} 1/(1 - x^(j^2)).
%C Total number of largest parts in all partitions of n into squares (A000290).
%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F G.f.: Sum_{i>=1} x^(i^2)/(1 - x^(i^2)) * Product_{j=1..i} 1/(1 - x^(j^2)).
%e a(9) = 13 because we have [9], [4, 4, 1], [4, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1] and 1 + 2 + 1 + 9 = 13.
%t nmax = 70; Rest[CoefficientList[Series[Sum[x^i^2/(1 - x^i^2) Product[1/(1 - x^j^2), {j, 1, i}], {i, 1, nmax}], {x, 0, nmax}], x]]
%o (PARI) x='x+O('x^71); Vec(sum(i=1, 71, x^(i^2)/(1 - x^(i^2)) * prod(j=1, i, 1/(1 - x^(j^2))))) \\ _Indranil Ghosh_, Apr 04 2017
%Y Cf. A000290, A001156, A046746, A092311, A281541, A284830.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Apr 03 2017
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