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A321752
Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of e(v) in p(u), where H is Heinz number, e is elementary symmetric functions, and p is power sum symmetric functions.
5
1, 1, -2, 1, 0, 1, 3, -3, 1, 0, -2, 1, -4, 2, 4, -4, 1, 0, 0, 1, 0, 4, 0, -4, 1, 0, 0, 3, -3, 1, 5, -5, -5, 5, 5, -5, 1, 0, 0, 0, -2, 1, -6, 6, 6, 3, -2, -6, -12, 9, 6, -6, 1, 0, -4, 0, 2, 4, -4, 1, 0, 0, -6, 6, 3, -5, 1, 0, 0, 0, 0, 1, 7, -7, -7, -7, 14, 7, 7
OFFSET
1,3
COMMENTS
Row n has length A000041(A056239(n)).
The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
EXAMPLE
Triangle begins:
1
1
-2 1
0 1
3 -3 1
0 -2 1
-4 2 4 -4 1
0 0 1
0 4 0 -4 1
0 0 3 -3 1
5 -5 -5 5 5 -5 1
0 0 0 -2 1
-6 6 6 3 -2 -6 -12 9 6 -6 1
0 -4 0 2 4 -4 1
0 0 -6 6 3 -5 1
0 0 0 0 1
7 -7 -7 -7 14 7 7 7 -7 -7 -21 14 7 -7 1
0 0 0 4 0 -4 1
For example, row 15 gives: p(32) = -6e(32) + 6e(221) + 3e(311) - 5e(2111) + e(11111).
KEYWORD
sign,tabf
AUTHOR
Gus Wiseman, Nov 20 2018
STATUS
approved