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A321913
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Tetrangle where T(n,H(u),H(v)) is the coefficient of m(v) in h(u), where u and v are integer partitions of n, H is Heinz number, m is monomial symmetric functions, and h is homogeneous symmetric functions.
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1
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1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 3, 1, 3, 6, 1, 1, 1, 1, 1, 1, 3, 2, 4, 6, 1, 2, 2, 3, 4, 1, 4, 3, 7, 12, 1, 6, 4, 12, 24, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 1, 2, 3, 5, 4, 7, 10, 1, 3, 5, 11, 8, 18, 30, 1, 3, 4, 8, 7, 13, 20, 1, 4, 7, 18, 13, 33, 60, 1, 5
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OFFSET
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1,5
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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 e(u), where f is forgotten symmetric functions and e is elementary symmetric functions.
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LINKS
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EXAMPLE
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Tetrangle begins:
(1): 1
.
(2): 1 1
(11): 1 2
.
(3): 1 1 1
(21): 1 2 3
(111): 1 3 6
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(4): 1 1 1 1 1
(22): 1 3 2 4 6
(31): 1 2 2 3 4
(211): 1 4 3 7 12
(1111): 1 6 4 12 24
.
(5): 1 1 1 1 1 1 1
(41): 1 2 2 3 3 4 5
(32): 1 2 3 5 4 7 10
(221): 1 3 5 11 8 18 30
(311): 1 3 4 8 7 13 20
(2111): 1 4 7 18 13 33 60
(11111): 1 5 10 30 20 60 20
For example, row 14 gives: h(32) = m(5) + 3m(32) + 2m(41) + 5m(221) + 4m(311) + 7m(2111) + 10m(11111).
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CROSSREFS
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This is a regrouping of the triangle A321744.
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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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