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A321912 Tetrangle where T(n,H(u),H(v)) is the coefficient of m(v) in e(u), where u and v are integer partitions of n, H is Heinz number, m is monomial symmetric functions, and e is elementary symmetric functions. 24
1, 0, 1, 1, 2, 0, 0, 1, 0, 1, 3, 1, 3, 6, 0, 0, 0, 0, 1, 0, 1, 0, 2, 6, 0, 0, 0, 1, 4, 0, 2, 1, 5, 12, 1, 6, 4, 12, 24, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 5, 0, 0, 0, 1, 0, 3, 10, 0, 0, 1, 5, 2, 12, 30, 0, 0, 0, 2, 1, 7, 20, 0, 1, 3, 12, 7, 27, 60, 1, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
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 h(u), where f is forgotten symmetric functions and h is homogeneous symmetric functions.
LINKS
EXAMPLE
Tetrangle begins (zeroes not shown):
(1): 1
.
(2): 1
(11): 1 2
.
(3): 1
(21): 1 3
(111): 1 3 6
.
(4): 1
(22): 1 2 6
(31): 1 4
(211): 2 1 5 12
(1111): 1 6 4 12 24
.
(5): 1
(41): 1 5
(32): 1 3 10
(221): 1 5 2 12 30
(311): 2 1 7 20
(2111): 1 3 12 7 27 60
(11111): 1 5 10 30 20 60 20
For example, row 14 gives: e(32) = m(221) + 3m(2111) + 10m(11111).
CROSSREFS
This is a regrouping of the triangle A321742.
Sequence in context: A321742 A228716 A029430 * A329921 A092303 A329343
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Nov 22 2018
STATUS
approved

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