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A325616
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Triangle read by rows where T(n,k) is the number of length-k integer partitions of n into factorial numbers.
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10
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1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 2, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 2, 2, 1
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OFFSET
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0,61
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LINKS
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FORMULA
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T(n,k) is the coefficient of x^n * y^k in the expansion of Product_{i > 0} 1/(1 - y * x^(i!)).
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EXAMPLE
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Triangle begins:
1
0 1
0 1 1
0 0 1 1
0 0 1 1 1
0 0 0 1 1 1
0 1 0 1 1 1 1
0 0 1 0 1 1 1 1
0 0 1 1 1 1 1 1 1
0 0 0 1 1 1 1 1 1 1
0 0 0 1 1 2 1 1 1 1 1
0 0 0 0 1 1 2 1 1 1 1 1
0 0 1 0 1 1 2 2 1 1 1 1 1
0 0 0 1 0 1 1 2 2 1 1 1 1 1
0 0 0 1 1 1 1 2 2 2 1 1 1 1 1
0 0 0 0 1 1 1 1 2 2 2 1 1 1 1 1
0 0 0 0 1 1 2 1 2 2 2 2 1 1 1 1 1
0 0 0 0 0 1 1 2 1 2 2 2 2 1 1 1 1 1
0 0 0 1 0 1 1 2 2 2 2 2 2 2 1 1 1 1 1
0 0 0 0 1 0 1 1 2 2 2 2 2 2 2 1 1 1 1 1
0 0 0 0 1 1 1 1 2 2 3 2 2 2 2 2 1 1 1 1 1
Row n = 12 counts the following partitions:
(66)
(6222)
(62211)
(222222) (621111)
(2222211) (6111111)
(22221111)
(222111111)
(2211111111)
(21111111111)
(111111111111)
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MATHEMATICA
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Table[SeriesCoefficient[Product[1/(1-y*x^(i!)), {i, 1, n}], {x, 0, n}, {y, 0, k}], {n, 0, 15}, {k, 0, n}]
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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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