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A279951
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Expansion of Product_{k>=1} 1/(1 - x^((k*(k+1)/2)^2)).
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0
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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, 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, 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
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OFFSET
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0,10
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COMMENTS
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Number of partitions of n into nonzero squared triangular numbers (A000537).
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LINKS
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Table of n, a(n) for n=0..105.
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
Wikipedia, Squared triangular number
Index entries for related partition-counting sequences
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FORMULA
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G.f.: Product_{k>=1} 1/(1 - x^((k*(k+1)/2)^2)).
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EXAMPLE
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a(10) = 2 because we have [9, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1].
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MATHEMATICA
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nmax = 105; 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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Cf. A000537, A007294, A068980.
Sequence in context: A133879 A343609 A054898 * A279224 A167383 A167661
Adjacent sequences: A279948 A279949 A279950 * A279952 A279953 A279954
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, Dec 23 2016
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STATUS
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approved
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