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%I #15 Sep 15 2021 03:19:26
%S 1,0,0,1,2,0,0,0,1,2,0,0,2,3,0,1,2,0,0,2,3,0,0,0,3,5,0,0,5,7,0,0,0,2,
%T 3,1,2,3,4,2,5,3,0,0,5,7,0,0,4,9,4,2,5,7,5,3,4,2,3,0,5,10,4,1,11,12,0,
%U 2,6,7,4,0,2,12,12,0,6,15,9,2,8,7,3,7,8,10,9,5,8,21,13,0,7,19,13,0,2,10,13,8
%N Expansion of Sum_{i>=1} x^(i^2)/(1 + x^(i^2)) * Product_{j>=1} (1 + x^(j^2)).
%C Total number of parts in all partitions of n into distinct squares.
%H Alois P. Heinz, <a href="/A281542/b281542.txt">Table of n, a(n) for n = 1..10000</a>
%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} (1 + x^(j^2)).
%F From _Alois P. Heinz_, Feb 03 2021: (Start)
%F a(n) = Sum_{k>=0} k * A341040(n,k).
%F a(n) = 0 <=> n in { A001422 }. (End)
%e a(26) = 5 because we have [25, 1], [16, 9 ,1] and 2 + 3 = 5.
%t nmax = 100; Rest[CoefficientList[Series[Sum[x^i^2/(1 + x^i^2), {i, 1, nmax}] Product[1 + x^j^2, {j, 1, nmax}], {x, 0, nmax}], x]]
%Y Cf. A000290, A001422, A015723, A033461, A317529, A341040.
%K nonn
%O 1,5
%A _Ilya Gutkovskiy_, Jan 23 2017
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