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A298858
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Number of ordered ways of writing n-th triangular number as a sum of n nonzero triangular numbers.
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10
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1, 1, 0, 0, 4, 11, 86, 777, 4670, 36075, 279482, 2345201, 21247326, 197065752, 1983741228, 20769081251, 228078253168, 2604226354265, 30880251148086, 379415992755572, 4818158748326064, 63116999199457944, 851467484377802094, 11811530978240316682, 168243449082524484856
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OFFSET
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0,5
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LINKS
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FORMULA
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a(n) = [x^(n*(n+1)/2)] (Sum_{k>=1} x^(k*(k+1)/2))^n.
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EXAMPLE
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a(4) = 4 because fourth triangular number is 10 and we have [3, 3, 3, 1], [3, 3, 1, 3], [3, 1, 3, 3] and [1, 3, 3, 3].
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MATHEMATICA
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Table[SeriesCoefficient[(EllipticTheta[2, 0, Sqrt[x]]/(2 x^(1/8)) - 1)^n, {x, 0, n (n + 1)/2}], {n, 0, 24}]
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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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