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A321929
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Tetrangle where T(n,H(u),H(v)) is the coefficient of f(v) in s(u), where u and v are integer partitions of n, H is Heinz number, f is forgotten symmetric functions, and s is Schur functions.
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0
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1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 2, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 2, 0, 0, 0, 1, 3, 0, 1, 1, 2, 3, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 4, 0, 0, 0, 1, 0, 2, 5, 0, 0, 1, 2, 1, 3, 5, 0, 0, 0, 1, 1, 3, 6, 0, 1, 1, 2, 2, 3, 4, 1, 1, 1, 1, 1, 1
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OFFSET
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1,11
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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 (zeros not shown):
(1): 1
.
(2): 1
(11): 1 1
.
(3): 1
(21): 1 2
(111): 1 1 1
.
(4): 1
(22): 1 1 2
(31): 1 3
(211): 1 1 2 3
(1111): 1 1 1 1 1
.
(5): 1
(41): 1 4
(32): 1 2 5
(221): 1 2 1 3 5
(311): 1 1 3 6
(2111): 1 1 2 2 3 4
(11111): 1 1 1 1 1 1 1
For example, row 14 gives: s(32) = f(221) + 2f(2111) + 5f(11111).
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CROSSREFS
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This is a regrouping of the triangle A321892.
Cf. A008480, A056239, A124794, A124795, A153452, A215366, A296188, A300121, A319191, A319193, A321912-A321935.
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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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approved
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