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A279221
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Expansion of Product_{k>=1} 1/(1 - x^(k^2*(k+1)/2)).
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7
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1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 12, 12, 12, 12, 13, 13, 16, 16, 16, 16, 17, 17, 20, 20, 20, 20, 21, 21, 25, 25, 25, 25, 27, 27, 31, 31, 31, 31, 33, 33, 37, 37, 37, 37, 39, 39, 44, 44, 44, 45, 48, 48, 53, 53, 54, 55, 58, 58, 63, 63, 64, 65, 68, 68, 74
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OFFSET
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0,7
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COMMENTS
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Number of partitions of n into nonzero pentagonal pyramidal numbers (A002411).
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LINKS
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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]
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FORMULA
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G.f.: Product_{k>=1} 1/(1 - x^(k^2*(k+1)/2)).
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EXAMPLE
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a(7) = 2 because we have [6, 1] and [1, 1, 1, 1, 1, 1, 1].
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MATHEMATICA
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nmax=90; CoefficientList[Series[Product[1/(1 - x^(k^2 (k + 1)/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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