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A321930
Tetrangle where T(n,H(u),H(v)) is the coefficient of s(v) in f(u), where u and v are integer partitions of n, H is Heinz number, f is forgotten symmetric functions, and s is Schur functions.
0
1, -1, 1, 1, 0, 1, -1, 1, -2, 1, 0, 1, 0, 0, -1, 0, 1, -1, 1, 1, 1, -1, 0, 0, 2, -1, -1, 1, 0, -3, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, -1, 0, 0, 1, -1, 1, -2, 1, 1, -1, -1, 1, 0, -2, 2, -1, 1, -1, 0, 0, 3, -2, 1, 0, 0, 0, 0, 3, -1, -1, 0, 1, 0, 0, -4, 1, 0, 0, 0, 0
OFFSET
1,9
COMMENTS
The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
EXAMPLE
Tetrangle begins (zeros not shown):
(1): 1
.
(2): -1 1
(11): 1
.
(3): 1 -1 1
(21): -2 1
(111): 1
.
(4): -1 1 -1 1
(22): 1 1 -1
(31): 2 -1 -1 1
(211): -3 1
(1111): 1
.
(5): 1 -1 1 -1 1
(41): -2 1 1 -1 -1 1
(32): -2 2 -1 1 -1
(221): 3 -2 1
(311): 3 -1 -1 1
(2111): -4 1
(11111): 1
For example, row 14 gives: f(32) = -2s(5) - s(32) + 2s(41) + s(221) - s(311).
CROSSREFS
This is a regrouping of the triangle A321894.
Sequence in context: A073423 A219180 A179952 * A134023 A257931 A325699
KEYWORD
sign,tabf
AUTHOR
Gus Wiseman, Nov 23 2018
STATUS
approved