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A321916
Tetrangle where T(n,H(u),H(v)) is the coefficient of e(v) in h(u), where u and v are integer partitions of n, H is Heinz number, e is elementary symmetric functions, and h is homogeneous symmetric functions.
0
1, -1, 1, 0, 1, 1, -2, 1, 0, -1, 1, 0, 0, 1, -1, 1, 2, -3, 1, 0, 1, 0, -2, 1, 0, 0, 1, -2, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 1, 1, -2, -2, 3, 3, -4, 1, 0, -1, 0, 1, 2, -3, 1, 0, 0, -1, 2, 1, -3, 1, 0, 0, 0, 1, 0, -2, 1, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, -1, 1
OFFSET
1,7
COMMENTS
The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
Also the coefficient of h(v) in e(u).
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 -2 1
(31): 1 -2 1
(211): -1 1
(1111): 1
.
(5): 1 -2 -2 3 3 -4 1
(41): -1 1 2 -3 1
(32): -1 2 1 -3 1
(221): 1 -2 1
(311): 1 -2 1
(2111): -1 1
(11111): 1
For example, row 14 gives: h(32) = -e(32) + 2e(221) + e(311) - 3e(2111) + e(11111).
CROSSREFS
This is a regrouping of the triangle A321749. Row sums are A134286.
Sequence in context: A016102 A083905 A179319 * A257265 A045706 A045634
KEYWORD
sign,tabf
AUTHOR
Gus Wiseman, Nov 22 2018
STATUS
approved