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A321923 Tetrangle where T(n,H(u),H(v)) is the coefficient of s(v) in h(u), where u and v are integer partitions of n, H is Heinz number, s is Schur functions, and h is homogeneous symmetric functions. 0
1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 2, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 2, 1, 0, 1, 2, 3, 3, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 2, 1, 1, 0, 0, 1, 2, 1, 0, 1, 0, 0, 1, 3, 3, 2, 3, 1, 0, 1, 4, 5, 5, 6, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,13
COMMENTS
The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
LINKS
EXAMPLE
Tetrangle begins (zeroes not shown):
(1): 1
.
(2): 1
(11): 1 1
.
(3): 1
(21): 1 1
(111): 1 2 1
.
(4): 1
(22): 1 1 1
(31): 1 1
(211): 1 1 2 1
(1111): 1 2 3 3 1
.
(5): 1
(41): 1 1
(32): 1 1 1
(221): 1 2 2 1 1
(311): 1 2 1 1
(2111): 1 3 3 2 3 1
(11111): 1 4 5 5 6 4 1
For example, row 14 gives: h(32) = s(5) + s(32) + s(41).
CROSSREFS
This is a regrouping of the triangle A321759.
Sequence in context: A175134 A027355 A127326 * A064663 A025923 A351358
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Nov 22 2018
STATUS
approved

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Last modified March 5 10:18 EST 2024. Contains 370548 sequences. (Running on oeis4.)