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A321915 Tetrangle where T(n,H(u),H(v)) is the coefficient of h(v) in m(u), where u and v are integer partitions of n, H is Heinz number, m is monomial symmetric functions, and h is homogeneous symmetric functions. 0
1, 2, -1, -1, 1, 3, -3, 1, -3, 5, -2, 1, -2, 1, 4, -2, -4, 4, -1, -2, 3, 2, -4, 1, -4, 2, 7, -7, 2, 4, -4, -7, 10, -3, -1, 1, 2, -3, 1, 5, -5, -5, 5, 5, -5, 1, -5, 9, 5, -7, -9, 9, -2, -5, 5, 11, -11, -8, 10, -2, 5, -7, -11, 14, 10, -14, 3, 5, -9, -8, 10, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
Also the coefficient of e(v) in f(u), where f is forgotten symmetric functions and e is elementary symmetric functions.
LINKS
EXAMPLE
Tetrangle begins:
(1): 1
.
(2): 2 -1
(11): -1 1
.
(3): 3 -3 1
(21): -3 5 -2
(111): 1 -2 1
.
(4): 4 -2 -4 4 -1
(22): -2 3 2 -4 1
(31): -4 2 7 -7 2
(211): 4 -4 -7 10 -3
(1111): -1 1 2 -3 1
.
(5): 5 -5 -5 5 5 -5 1
(41): -5 9 5 -7 -9 9 -2
(32): -5 5 11 11 -8 10 -2
(221): 5 -7 11 14 10 14 3
(311): 5 -9 -8 10 12 13 3
(2111): -5 9 10 14 13 17 -4
(11111): 1 -2 -2 3 3 -4 1
For example, row 14 gives: m(32) = -5h(5) + 11h(32) + 5h(41) - 11h(221) - 8h(311) + 10h(2111) - 2h(11111).
CROSSREFS
This is a regrouping of the triangle A321748. Row sums are A155972.
Sequence in context: A302538 A228428 A344911 * A321748 A263447 A180303
KEYWORD
sign,tabf
AUTHOR
Gus Wiseman, Nov 22 2018
STATUS
approved

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)