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A321922
Tetrangle where T(n,H(u),H(v)) is the coefficient of h(v) in s(u), where u and v are integer partitions of n, H is Heinz number, h is homogeneous symmetric functions, and s is Schur functions.
0
1, 1, 0, -1, 1, 1, 0, 0, -1, 1, 0, 1, -2, 1, 1, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 0, 1, 0, 0, 1, -1, -1, 1, 0, -1, 1, 2, -3, 1, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 1, -1, 1, -1, 0, 0, 1, -1, -1, 0, 1, 0, 0, -1, 1, 2, -2, -1, 1, 0
OFFSET
1,13
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
(11): -1 1
.
(3): 1
(21): -1 1
(111): 1 -2 1
.
(4): 1
(22): 1 -1
(31): -1 1
(211): 1 -1 -1 1
(1111): -1 1 2 -3 1
.
(5): 1
(41): -1 1
(32): -1 1
(221): 1 -1 1 -1
(311): 1 -1 -1 1
(2111): -1 1 2 -2 -1 1
(11111): 1 -2 -2 3 3 -4 1
For example, row 14 gives: s(32) = h(32) - h(41).
CROSSREFS
Row sums are A155972. This is a regrouping of the triangle A321758.
Sequence in context: A203905 A309142 A064532 * A362496 A360003 A287146
KEYWORD
sign,tabf
AUTHOR
Gus Wiseman, Nov 22 2018
STATUS
approved