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A321894
Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of s(v) in f(u), where H is Heinz number, f is forgotten symmetric functions, and s is Schur functions.
1
1, 1, -1, 1, 1, 0, 1, -1, 1, -2, 1, 0, -1, 0, 1, -1, 1, 1, 0, 0, 1, 1, -1, 0, 0, 2, -1, -1, 1, 0, 1, -1, 0, 0, 1, -1, 1, -3, 0, 1, 0, 0, -1, 0, 1, 0, 0, -1, 0, 0, 1, -1, 1, -2, 1, 1, -1, -1, 1, 0, -2, 2, -1, 1, -1, 0, 0
OFFSET
1,10
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
1 0
1 -1 1
-2 1 0
-1 0 1 -1 1
1 0 0
1 1 -1 0 0
2 -1 -1 1 0
1 -1 0 0 1 -1 1
-3 0 1 0 0
-1 0 1 0 0 -1 0 0 1 -1 1
-2 1 1 -1 -1 1 0
-2 2 -1 1 -1 0 0
For example, row 15 gives: f(32) = -2s(5) - s(32) + 2s(41) + s(221) - s(311).
KEYWORD
sign,tabf,more
AUTHOR
Gus Wiseman, Nov 20 2018
STATUS
approved