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A321927
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Tetrangle where T(n,H(u),H(v)) is the coefficient of m(v) in f(u), where u and v are integer partitions of n, H is Heinz number, m is monomial symmetric functions, and f is forgotten symmetric functions.
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0
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1, -1, 0, 1, 1, 1, 0, 0, -2, -1, 0, 1, 1, 1, -1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 1, 0, 0, -3, -2, -2, -1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 3, 1, 2, 1, 0, 0, 0, 3, 2, 1, 0, 1, 0, 0, -4, -3, -3, -2, -2, -1, 0
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OFFSET
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1,9
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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 f(v) in m(u).
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LINKS
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EXAMPLE
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Tetrangle begins (zeroes not shown):
(1): 1
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(2): -1
(11): 1 1
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(3): 1
(21): -2 -1
(111): 1 1 1
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(4): -1
(22): 1 1
(31): 2 1
(211): -3 -2 -2 -1
(1111): 1 1 1 1 1
.
(5): 1
(41): -2 -1
(32): -2 -1
(221): 3 1 2 1
(311): 3 2 1 1
(2111): -4 -3 -3 -2 -2 -1
(11111): 1 1 1 1 1 1 1
For example, row 14 gives: f(32) = -2m(5) - m(32).
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CROSSREFS
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This is a regrouping of the triangle A321886.
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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