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A298435
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Expansion of Product_{k>=1} 1/(1 - x^(k*(k+1)/2))^2.
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4
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1, 2, 3, 6, 9, 12, 20, 28, 36, 52, 70, 88, 120, 156, 192, 250, 318, 386, 488, 606, 727, 900, 1101, 1308, 1590, 1916, 2257, 2706, 3225, 3768, 4465, 5270, 6117, 7178, 8399, 9686, 11274, 13094, 15020, 17352, 20017, 22846, 26230, 30080, 34175, 39010, 44500, 50346, 57184, 64914, 73156
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OFFSET
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0,2
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COMMENTS
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Number of partitions of n into triangular numbers of 2 kinds.
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LINKS
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FORMULA
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G.f.: Product_{k>=1} 1/(1 - x^(k*(k+1)/2))^2.
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
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EXAMPLE
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a(3) = 6 because we have [3a], [3b], [1a, 1a, 1a], [1a, 1a, 1b], [1a, 1b, 1b] and [1b, 1b, 1b].
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MATHEMATICA
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nmax = 50; CoefficientList[Series[Product[1/(1 - x^(k (k + 1)/2))^2, {k, 1, nmax}], {x, 0, nmax}], x]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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