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A321919
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Tetrangle where T(n,H(u),H(v)) is the coefficient of h(v) in p(u), where u and v are integer partitions of n, H is Heinz number, h is homogeneous symmetric functions, and p is power sum symmetric functions.
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0
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1, 2, -1, 0, 1, 3, -3, 1, 0, 2, -1, 0, 0, 1, 4, -2, -4, 4, -1, 0, 4, 0, -4, 1, 0, 0, 3, -3, 1, 0, 0, 0, 2, -1, 0, 0, 0, 0, 1, 5, -5, -5, 5, 5, -5, 1, 0, 4, 0, -2, -4, 4, -1, 0, 0, 6, -6, -3, 5, -1, 0, 0, 0, 4, 0, -4, 1, 0, 0, 0, 0, 3, -3, 1, 0, 0, 0, 0, 0, 2
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OFFSET
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1,2
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COMMENTS
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The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
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LINKS
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EXAMPLE
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Tetrangle begins (zeroes not shown):
(1): 1
.
(2): 2 -1
(11): 1
.
(3): 3 -3 1
(21): 2 -1
(111): 1
.
(4): 4 -2 -4 4 -1
(22): 4 -4 1
(31): 3 -3 1
(211): 2 -1
(1111): 1
.
(5): 5 -5 -5 5 5 -5 1
(41): 4 -2 -4 4 -1
(32): 6 -6 -3 5 -1
(221): 4 -4 1
(311): 3 -3 1
(2111): 2 -1
(11111): 1
For example, row 14 gives: p(32) = 6h(32) - 6h(221) - 3h(311) + 5h(2111) - h(11111).
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CROSSREFS
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This is a regrouping of the triangle A321754.
Cf. A005651, A008480, A056239, A124794, A124795, A215366, A318284, A318360, A319191, A319193, A321912-A321935.
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KEYWORD
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sign,tabf
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AUTHOR
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STATUS
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approved
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