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A321932
Tetrangle where T(n,H(u),H(v)) is the coefficient of p(v) in e(u) * Product_i u_i!, where u and v are integer partitions of n, H is Heinz number, p is power sum symmetric functions, and e is elementary symmetric functions.
0
1, -1, 1, 0, 1, 2, -3, 1, 0, -1, 1, 0, 0, 1, -6, 3, 8, -6, 1, 0, 1, 0, -2, 1, 0, 0, 2, -3, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 1, 24, -30, -20, 15, 20, -10, 1, 0, -6, 0, 3, 8, -6, 1, 0, 0, -2, 3, 2, -4, 1, 0, 0, 0, 1, 0, -2, 1, 0, 0, 0, 0, 2, -3, 1, 0, 0, 0, 0, 0
OFFSET
1,6
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): 2 -3 1
(21): -1 1
(111): 1
.
(4): -6 3 8 -6 1
(22): 1 -2 1
(31): 2 -3 1
(211): -1 1
(1111): 1
.
(5): 24 30 20 15 20 10 1
(41): -6 3 8 -6 1
(32): -2 3 2 -4 1
(221): 1 -2 1
(311): 2 -3 1
(2111): -1 1
(11111): 1
For example, row 14 gives: 12e(32) = -2p(32) + 3p(221) + 2p(311) - 4p(2111) + p(11111).
CROSSREFS
Row sums are A134286. This is a regrouping of the triangle A321896.
Sequence in context: A124314 A059087 A353493 * A321933 A030373 A079343
KEYWORD
sign,tabf
AUTHOR
Gus Wiseman, Nov 23 2018
STATUS
approved