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A321755
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Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of e(v) in s(u), where H is Heinz number, e is elementary symmetric functions, and s is Schur functions.
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1
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1, 1, -1, 1, 1, 0, 1, -2, 1, -1, 1, 0, -1, 1, 2, -3, 1, 1, 0, 0, 0, 1, -1, 0, 0, 1, -1, -1, 1, 0, 1, -2, -2, 3, 3, -4, 1, -1, 0, 1, 0, 0, -1, 2, 2, 1, -1, -3, -6, 6, 4, -5, 1, -1, 1, 2, -2, -1, 1, 0, 0, 1, -1, 1, -1, 0, 0, 1, 0, 0, 0, 0, 1, -2, -2, -2, 6, 3, 3
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OFFSET
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1,8
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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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Triangle begins:
1
1
-1 1
1 0
1 -2 1
-1 1 0
-1 1 2 -3 1
1 0 0
0 1 -1 0 0
1 -1 -1 1 0
1 -2 -2 3 3 -4 1
-1 0 1 0 0
-1 2 2 1 -1 -3 -6 6 4 -5 1
-1 1 2 -2 -1 1 0
0 1 -1 1 -1 0 0
1 0 0 0 0
1 -2 -2 -2 6 3 3 3 -4 -4 -12 10 5 -6 1
0 -1 1 0 0 0 0
For example, row 14 gives: s(41) = -e(5) + 2e(32) + e(41) - 2e(221) - e(311) + e(2111).
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CROSSREFS
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Cf. A000085, A008480, A056239, A082733, A124795, A153452, A296188, A300121, A304438, A317552, A317554, A321742-A321765.
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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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