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A321918
Tetrangle where T(n,H(u),H(v)) is the coefficient of e(v) in p(u), where u and v are integer partitions of n, H is Heinz number, e is elementary symmetric functions, and p is power sum symmetric functions.
5
1, -2, 1, 0, 1, 3, -3, 1, 0, -2, 1, 0, 0, 1, -4, 2, 4, -4, 1, 0, 4, 0, -4, 1, 0, 0, 3, -3, 1, 0, 0, 0, -2, 1, 0, 0, 0, 0, 1, 5, -5, -5, 5, 5, -5, 1, 0, -4, 0, 2, 4, -4, 1, 0, 0, -6, 6, 3, -5, 1, 0, 0, 0, 4, 0, -4, 1, 0, 0, 0, 0, 3, -3, 1, 0, 0, 0, 0, 0, -2, 1
OFFSET
1,2
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): -2 1
(11): 1
.
(3): 3 -3 1
(21): -2 1
(111): 1
.
(4): -4 2 4 -4 1
(22): 4 -4 1
(31): 3 -3 1
(211): -2 1
(1111): 1
.
(5): 5 -5 -5 5 5 -5 1
(41): -4 2 4 -4 1
(32): -6 6 3 -5 1
(221): 4 -4 1
(311): 3 -3 1
(2111): -2 1
(11111): 1
For example, row 14 gives: p(32) = -6e(32) + 6e(221) + 3e(311) - 5e(2111) + e(11111).
CROSSREFS
This is a regrouping of the triangle A321752.
Sequence in context: A274581 A353279 A321919 * A321754 A321752 A349839
KEYWORD
sign,tabf
AUTHOR
Gus Wiseman, Nov 22 2018
STATUS
approved