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%I #7 Apr 08 2018 06:52:57
%S 1,2,3,6,9,12,20,28,36,52,70,88,120,156,192,250,318,386,488,606,727,
%T 900,1101,1308,1590,1916,2257,2706,3225,3768,4465,5270,6117,7178,8399,
%U 9686,11274,13094,15020,17352,20017,22846,26230,30080,34175,39010,44500,50346,57184,64914,73156
%N Expansion of Product_{k>=1} 1/(1 - x^(k*(k+1)/2))^2.
%C Number of partitions of n into triangular numbers of 2 kinds.
%C Self-convolution of A007294.
%H Vaclav Kotesovec, <a href="/A298435/b298435.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Par#part">Index entries for related partition-counting sequences</a>
%F G.f.: Product_{k>=1} 1/(1 - x^(k*(k+1)/2))^2.
%F a(n) ~ exp(3*(Pi/2)^(1/3) * Zeta(3/2)^(2/3) * n^(1/3)) * Zeta(3/2)^(5/3) / (2^(29/6) * sqrt(3) * Pi^(5/3) * n^(13/6)). - _Vaclav Kotesovec_, Apr 08 2018
%e a(3) = 6 because we have [3a], [3b], [1a, 1a, 1a], [1a, 1a, 1b], [1a, 1b, 1b] and [1b, 1b, 1b].
%t nmax = 50; CoefficientList[Series[Product[1/(1 - x^(k (k + 1)/2))^2, {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A000217, A000712, A007294, A279225.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Jan 19 2018
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