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A280129 Expansion of Product_{k>=2} (1 + x^(k^2)).

%I A280129 #12 Dec 27 2016 13:21:31
%S A280129 1,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,2,0,0,0,2,0,0,0,0,
%T A280129 1,0,1,0,1,0,1,1,0,0,0,2,0,0,0,2,1,0,1,1,1,0,1,0,1,0,0,2,1,0,1,3,0,0,
%U A280129 1,1,1,0,0,1,3,0,0,2,2,0,1,2,0,1,1,2,1
%N A280129 Expansion of Product_{k>=2} (1 + x^(k^2)).
%C A280129 Number of partitions of n into distinct squares > 1.
%H A280129 Vaclav Kotesovec, <a href="/A280129/b280129.txt">Table of n, a(n) for n = 0..10000</a>
%H A280129 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%H A280129 <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F A280129 G.f.: Product_{k>=2} (1 + x^(k^2)).
%F A280129 From _Vaclav Kotesovec_, Dec 26 2016: (Start)
%F A280129 a(n) = Sum_{k=0..n} (-1)^(n-k) * A033461(k).
%F A280129 a(n) + a(n-1) = A033461(n).
%F A280129 a(n) ~ A033461(n)/2.
%F A280129 (End)
%e A280129 G.f. = 1 + x^4 + x^9 + x^13 + x^16 + x^20 + 2*x^25 + 2*x^29 + x^34 + x^36 + ...
%e A280129 a(25) = 2 because we have [25] and [16, 9].
%t A280129 nmax = 115; CoefficientList[Series[Product[1 + x^k^2, {k, 2, nmax}], {x, 0, nmax}], x]
%o A280129 (PARI) {a(n) = if(n < 0, 0, polcoeff( prod(k=2, sqrtint(n), 1 + x^k^2 + x*O(x^n)), n))}; /* _Michael Somos_, Dec 26 2016 */
%Y A280129 Cf. A001156, A033461, A078134.
%K A280129 nonn
%O A280129 0,26
%A A280129 _Ilya Gutkovskiy_, Dec 26 2016