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A321746 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of e(v) in m(u), where H is Heinz number, m is monomial symmetric functions, and e is elementary symmetric functions. 2
1, 1, -2, 1, 1, 0, 3, -3, 1, -3, 1, 0, -4, 2, 4, -4, 1, 1, 0, 0, 2, 1, -2, 0, 0, 4, -2, -1, 1, 0, 5, -5, -5, 5, 5, -5, 1, -4, 0, 1, 0, 0, -6, 6, 6, 3, -2, -6, -12, 9, 6, -6, 1, -5, 1, 5, -3, -1, 1, 0, -5, 5, -1, 1, -2, 0, 0, 1, 0, 0, 0, 0, 7, -7, -7, -7, 14, 7 (list; graph; refs; listen; history; text; internal format)
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).
Also the coefficient of h(v) in f(u), where h is homogeneous symmetric functions and f is forgotten symmetric functions.
LINKS
EXAMPLE
Triangle begins:
1
1
-2 1
1 0
3 -3 1
-3 1 0
-4 2 4 -4 1
1 0 0
2 1 -2 0 0
4 -2 -1 1 0
5 -5 -5 5 5 -5 1
-4 0 1 0 0
-6 6 6 3 -2 -6 -12 9 6 -6 1
-5 1 5 -3 -1 1 0
-5 5 -1 1 -2 0 0
1 0 0 0 0
7 -7 -7 -7 14 7 7 7 -7 -7 -21 14 7 -7 1
5 -3 1 0 0 0 0
For example, row 10 gives: m(31) = 4e(4) - 2e(22) - e(31) + e(211).
CROSSREFS
Row sums are A321747.
Sequence in context: A300756 A347062 A321914 * A133830 A316632 A111571
KEYWORD
sign,tabf
AUTHOR
Gus Wiseman, Nov 19 2018
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)