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%I #5 Dec 02 2020 09:01:15
%S 0,1,0,2,0,2,1,3,1,4,3,4,4,6,5,9,7,10,9,14,10,19,15,21,18,27,22,34,30,
%T 37,37,47,43,57,56,64,66,80,75,96,94,108,110,131,125,155,154,173,178,
%U 207,201,240,245,267,280,315,315,364,374,406,423,477,473,543,555,604
%N Number of partitions of n into an odd number of triangular numbers.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%F G.f.: (1/2) * (Product_{k>=1} 1 / (1 - x^(k*(k + 1)/2)) - Product_{k>=1} 1 / (1 + x^(k*(k + 1)/2))).
%F a(n) = (A007294(n) - A292519(n)) / 2.
%e a(7) = 3 because we have [3, 3, 1], [3, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1].
%t nmax = 65; CoefficientList[Series[(1/2) (Product[1/(1 - x^(k (k + 1)/2)), {k, 1, nmax}] - Product[1/(1 + x^(k (k + 1)/2)), {k, 1, nmax}]), {x, 0, nmax}], x]
%Y Cf. A000217, A007294, A027193, A292519, A339365, A339373, A339375, A339376.
%K nonn
%O 0,4
%A _Ilya Gutkovskiy_, Dec 02 2020
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