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A321933
Tetrangle where T(n,H(u),H(v)) is the coefficient of p(v) in h(u) * Product_i u_i!, where u and v are integer partitions of n, H is Heinz number, p is power sum symmetric functions, and h is homogeneous symmetric functions.
0
1, 1, 1, 0, 1, 2, 3, 1, 0, 1, 1, 0, 0, 1, 6, 3, 8, 6, 1, 0, 1, 0, 2, 1, 0, 0, 2, 3, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 24, 30, 20, 15, 20, 10, 1, 0, 6, 0, 3, 8, 6, 1, 0, 0, 2, 3, 2, 4, 1, 0, 0, 0, 1, 0, 2, 1, 0, 0, 0, 0, 2, 3, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0
OFFSET
1,6
COMMENTS
The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
EXAMPLE
Tetrangle begins (zeros not shown):
(1): 1
.
(2): 1 1
(11): 1
.
(3): 2 3 1
(21): 1 1
(111): 1
.
(4): 6 3 8 6 1
(22): 1 2 1
(31): 2 3 1
(211): 1 1
(1111): 1
.
(5): 24 30 20 15 20 10 1
(41): 6 3 8 6 1
(32): 2 3 2 4 1
(221): 1 2 1
(311): 2 3 1
(2111): 1 1
(11111): 1
For example, row 14 gives: 12h(32) = 2p(32) + 3p(221) + 2p(311) + 4p(2111) + p(11111).
CROSSREFS
This is a regrouping of the triangle A321897.
Sequence in context: A059087 A353493 A321932 * A030373 A079343 A004566
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Nov 23 2018
STATUS
approved