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A292518
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Expansion of Product_{k>=1} (1 - x^(k*(k+1)/2)).
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8
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1, -1, 0, -1, 1, 0, -1, 1, 0, 1, -2, 1, 0, 1, -1, -1, 2, -1, 1, -2, 1, 0, 0, 0, 0, 1, -1, 1, -3, 2, -1, 2, -1, 0, 1, -1, 0, -2, 3, -1, 1, -2, 1, 1, -2, 0, 0, 2, 0, -1, 0, 2, -2, -1, -1, 1, 2, -1, 1, -1, 1, -2, 1, -2, 3, 1, -2, 0, -2, 3, -1, -1, 0, 3, -1, 0, -2, 1, 0, -3, 2, 2, 1, -1, -1, 0, 0, -1, 0, 2, -1
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OFFSET
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0,11
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COMMENTS
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Convolution inverse of A007294.
The difference between the number of partitions of n into an even number of distinct triangular numbers and the number of partitions of n into an odd number of distinct triangular numbers.
Euler transform of {-1 if n is a triangular number else 0, n > 0} = -A010054. - Gus Wiseman, Oct 22 2018
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 0..10000
Index entries for related partition-counting sequences
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FORMULA
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G.f.: Product_{k>=1} (1 - x^(k*(k+1)/2)).
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MATHEMATICA
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nmax = 90; CoefficientList[Series[Product[1 - x^(k (k + 1)/2), {k, 1, nmax}], {x, 0, nmax}], x]
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CROSSREFS
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Product_{k>=1} (1 - x^(k*((m-2)*k-(m-4))/2)): this sequence (m=3), A276516 (m=4), A305355 (m=5).
Cf. A007294, A010054, A024940, A280366, A320767, A320784.
Sequence in context: A187360 A334368 A240718 * A264997 A222759 A024940
Adjacent sequences: A292515 A292516 A292517 * A292519 A292520 A292521
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KEYWORD
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sign
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AUTHOR
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Ilya Gutkovskiy, Sep 18 2017
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STATUS
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approved
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