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A321896
Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of p(v) in e(u) * Product_i u_i!, where H is Heinz number, e is elementary symmetric functions, and p is power sum symmetric functions.
2
1, 1, -1, 1, 0, 1, 2, -3, 1, 0, -1, 1, -6, 3, 8, -6, 1, 0, 0, 1, 0, 1, 0, -2, 1, 0, 0, 2, -3, 1, 24, -30, -20, 15, 20, -10, 1, 0, 0, 0, -1, 1, -120, 90, 144, 40, -15, -90, -120, 45, 40, -15, 1, 0, -6, 0, 3, 8, -6, 1, 0, 0, -2, 3, 2, -4, 1, 0, 0, 0, 0, 1, 720
OFFSET
1,7
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
-1 1
0 1
2 -3 1
0 -1 1
-6 3 8 -6 1
0 0 1
0 1 0 -2 1
0 0 2 -3 1
24 -30 -20 15 20 -10 1
0 0 0 -1 1
-120 90 144 40 -15 -90 -120 45 40 -15 1
0 -6 0 3 8 -6 1
0 0 -2 3 2 -4 1
0 0 0 0 1
720 -840 -504 -420 630 504 210 280 -105 -210 -420 105 70 -21 1
0 0 0 1 0 -2 1
For example, row 15 gives: 12e(32) = -2p(32) + 3p(221) + 2p(311) - 4p(2111) + p(11111).
KEYWORD
sign,tabf
AUTHOR
Gus Wiseman, Nov 20 2018
STATUS
approved