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A321920
Tetrangle where T(n,H(u),H(v)) is the coefficient of e(v) in s(u), where u and v are integer partitions of n, H is Heinz number, e is elementary symmetric functions, and s is Schur functions.
0
1, -1, 1, 1, 0, 1, -2, 1, -1, 1, 0, 1, 0, 0, -1, 1, 2, -3, 1, 0, 1, -1, 0, 0, 1, -1, -1, 1, 0, -1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, -2, -2, 3, 3, -4, 1, -1, 1, 2, -2, -1, 1, 0, 0, 1, -1, 1, -1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, -1, 0, 1, 0, 0, -1, 1, 0, 0, 0, 0
OFFSET
1,7
COMMENTS
The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
EXAMPLE
Tetrangle begins (zeroes not shown):
(1): 1
.
(2): -1 1
(11): 1
.
(3): 1 -2 1
(21): -1 1
(111): 1
.
(4): -1 1 2 -3 1
(22): 1 -1
(31): 1 -1 -1 1
(211): -1 1
(1111): 1
.
(5): 1 -2 -2 3 3 -4 1
(41): -1 1 2 -2 -1 1
(32): 1 -1 1 -1
(221): -1 1
(311): 1 -1 -1 1
(2111): -1 1
(11111): 1
For example, row 14 gives: s(32) = -e(32) + e(41) + e(221) - e(311).
CROSSREFS
Row sums are A134286. This is a regrouping of the triangle A321755.
Sequence in context: A210825 A056226 A044935 * A106276 A305053 A374081
KEYWORD
sign,tabf
AUTHOR
Gus Wiseman, Nov 22 2018
STATUS
approved