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A306489
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Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of 1/(1 - Sum_{d|k} x^d).
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0
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1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 2, 2, 5, 1, 1, 1, 1, 3, 3, 8, 1, 1, 1, 2, 1, 6, 4, 13, 1, 1, 1, 1, 4, 1, 10, 6, 21, 1, 1, 1, 2, 1, 7, 2, 18, 9, 34, 1, 1, 1, 1, 3, 1, 13, 3, 31, 13, 55, 1, 1, 1, 2, 2, 6, 1, 25, 4, 55, 19, 89, 1, 1, 1, 1, 3, 3, 10, 1, 46, 5, 96, 28, 144, 1
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OFFSET
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0,9
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COMMENTS
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A(n,k) is the number of compositions (ordered partitions) of n into divisors of k.
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LINKS
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FORMULA
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G.f. of column k: 1/(1 - Sum_{d|k} x^d).
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EXAMPLE
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Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, ...
1, 2, 1, 2, 1, 2, ...
1, 3, 2, 3, 1, 4, ...
1, 5, 3, 6, 1, 7, ...
1, 8, 4, 10, 2, 13, ...
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MATHEMATICA
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Table[Function[k, SeriesCoefficient[1/(1 - Sum[x^d, {d, Divisors[k]}]), {x, 0, n}]][i - n + 1], {i, 0, 12}, {n, 0, i}] // Flatten
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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