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A321927
Tetrangle where T(n,H(u),H(v)) is the coefficient of m(v) in f(u), where u and v are integer partitions of n, H is Heinz number, m is monomial symmetric functions, and f is forgotten symmetric functions.
0
1, -1, 0, 1, 1, 1, 0, 0, -2, -1, 0, 1, 1, 1, -1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 1, 0, 0, -3, -2, -2, -1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 3, 1, 2, 1, 0, 0, 0, 3, 2, 1, 0, 1, 0, 0, -4, -3, -3, -2, -2, -1, 0
OFFSET
1,9
COMMENTS
The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
Also the coefficient of f(v) in m(u).
EXAMPLE
Tetrangle begins (zeroes not shown):
(1): 1
.
(2): -1
(11): 1 1
.
(3): 1
(21): -2 -1
(111): 1 1 1
.
(4): -1
(22): 1 1
(31): 2 1
(211): -3 -2 -2 -1
(1111): 1 1 1 1 1
.
(5): 1
(41): -2 -1
(32): -2 -1
(221): 3 1 2 1
(311): 3 2 1 1
(2111): -4 -3 -3 -2 -2 -1
(11111): 1 1 1 1 1 1 1
For example, row 14 gives: f(32) = -2m(5) - m(32).
CROSSREFS
This is a regrouping of the triangle A321886.
Sequence in context: A065712 A153172 A242498 * A016194 A258139 A261887
KEYWORD
sign,tabf
AUTHOR
Gus Wiseman, Nov 22 2018
STATUS
approved