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%I #9 May 08 2017 00:28:35
%S 1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,
%T 4,4,6,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,10,10,10,10,10,10,10,10,10,
%U 12,12,12,12,12,12,12,12,12,15,15,15,15,15,15,15,15,15,18,18,18,18,18,18,18,18,18,21,21,21,21,21,21,21,21,21,24,25,25,25,25,25,25
%N Expansion of Product_{k>=1} 1/(1 - x^((k*(k+1)/2)^2)).
%C Number of partitions of n into nonzero squared triangular numbers (A000537).
%H M. Bernstein and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
%H M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Squared_triangular_number">Squared triangular number</a>
%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F G.f.: Product_{k>=1} 1/(1 - x^((k*(k+1)/2)^2)).
%e a(10) = 2 because we have [9, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1].
%t nmax = 105; CoefficientList[Series[Product[1/(1 - x^((k (k + 1)/2)^2)), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A000537, A007294, A068980.
%K nonn
%O 0,10
%A _Ilya Gutkovskiy_, Dec 23 2016
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