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A321923
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Tetrangle where T(n,H(u),H(v)) is the coefficient of s(v) in h(u), where u and v are integer partitions of n, H is Heinz number, s is Schur functions, and h is homogeneous symmetric functions.
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0
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1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 2, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 2, 1, 0, 1, 2, 3, 3, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 2, 1, 1, 0, 0, 1, 2, 1, 0, 1, 0, 0, 1, 3, 3, 2, 3, 1, 0, 1, 4, 5, 5, 6, 4
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OFFSET
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1,13
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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): 1
(11): 1 1
.
(3): 1
(21): 1 1
(111): 1 2 1
.
(4): 1
(22): 1 1 1
(31): 1 1
(211): 1 1 2 1
(1111): 1 2 3 3 1
.
(5): 1
(41): 1 1
(32): 1 1 1
(221): 1 2 2 1 1
(311): 1 2 1 1
(2111): 1 3 3 2 3 1
(11111): 1 4 5 5 6 4 1
For example, row 14 gives: h(32) = s(5) + s(32) + s(41).
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CROSSREFS
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This is a regrouping of the triangle A321759.
Cf. A005651, 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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