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A321914
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Tetrangle where T(n,H(u),H(v)) is the coefficient of e(v) in m(u), where u and v are integer partitions of n, H is Heinz number, m is monomial symmetric functions, and e is elementary symmetric functions.
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5
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1, -2, 1, 1, 0, 3, -3, 1, -3, 1, 0, 1, 0, 0, -4, 2, 4, -4, 1, 2, 1, -2, 0, 0, 4, -2, -1, 1, 0, -4, 0, 1, 0, 0, 1, 0, 0, 0, 0, 5, -5, -5, 5, 5, -5, 1, -5, 1, 5, -3, -1, 1, 0, -5, 5, -1, 1, -2, 0, 0, 5, -3, 1, 0, 0, 0, 0, 5, -1, -2, 0, 1, 0, 0, -5, 1, 0, 0, 0, 0
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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).
Also the coefficient of h(v) in f(u), where f is forgotten symmetric functions and h is homogeneous symmetric functions.
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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): -3 1
(111): 1
.
(4): -4 2 4 -4 1
(22): 2 1 -2
(31): 4 -2 -1 1
(211): -4 1
(1111): 1
.
(5): 5 -5 -5 5 5 -5 1
(41): -5 1 5 -3 -1 1
(32): -5 5 -1 1 -2
(221): 5 -3 1
(311): 5 -1 -2 1
(2111): -5 1
(11111): 1
For example, row 14 gives: m(32) = -5e(5) - e(32) + 5e(41) + e(221) - 2e(311).
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CROSSREFS
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This is a regrouping of the triangle A321746.
Cf. A005651, A008480, A056239, A124794, A124795, A215366, A318284, A318360, A319191, A319193, A321854, A321738, 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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