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A321888
Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of f(v) in p(u), where H is Heinz number, p is power sum symmetric functions, and f is forgotten symmetric functions.
2
1, 1, -1, 0, 1, 2, 1, 0, 0, -1, -1, 0, -1, 0, 0, 0, 0, 1, 3, 6, 1, 2, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, -2, -2, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 1, 6, 4, 12, 24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0
OFFSET
1,6
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).
Up to sign, a(n) is also the coefficient of m(v) in p(u), where m is monomial symmetric functions.
EXAMPLE
Triangle begins:
1
1
-1 0
1 2
1 0 0
-1 -1 0
-1 0 0 0 0
1 3 6
1 2 0 0 0
1 0 1 0 0
1 0 0 0 0 0 0
-1 -2 -2 -2 0
-1 0 0 0 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0
-1 0 -1 0 0 0 0
1 6 4 12 24
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 2 2 0 0 0
For example, row 12 gives: p(211) = -f(4) - 2f(22) - 2f(31) - 2f(211).
KEYWORD
sign,tabf
AUTHOR
Gus Wiseman, Nov 20 2018
STATUS
approved