A333144 revision #4
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A333144
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Irregular triangle where row n lists the product of the factorials of the exponentials of the partitions of n and the partitions are enumerated in canonical order.
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2
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1, 1, 1, 2, 1, 1, 6, 1, 1, 2, 2, 24, 1, 1, 1, 2, 2, 6, 120, 1, 1, 1, 2, 2, 1, 6, 6, 4, 24, 720, 1, 1, 1, 2, 1, 1, 6, 2, 2, 2, 24, 6, 12, 120, 5040, 1, 1, 1, 2, 1, 1, 6, 2, 1, 2, 2, 24, 2, 4, 2, 6, 120, 24, 12, 48, 720, 40320
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OFFSET
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0,4
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COMMENTS
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By 'canonical order' we understand the graded reverse lexicographic order (the default order of Mathematica and SageMath).
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LINKS
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EXAMPLE
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The irregular table starts:
[0] [1]
[1] [1]
[2] [1, 2]
[3] [1, 1, 6]
[4] [1, 1, 2, 2, 24]
[5] [1, 1, 1, 2, 2, 6, 120]
[6] [1, 1, 1, 2, 2, 1, 6, 6, 4, 24, 720]
[7] [1, 1, 1, 2, 1, 1, 6, 2, 2, 2, 24, 6, 12, 120, 5040]
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PROG
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(SageMath)
def A333144row(n):
return [product(factorial(expo) for expo in partition.to_exp()) for partition in Partitions(n)]
for n in (0..9): print(A333144row(n))
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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proposed
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