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Tetrangle where T(n,H(u),H(v)) is the coefficient of m(v) in p(u), where u and v are integer partitions of n, H is Heinz number, m is monomial symmetric functions, and p is power sum symmetric functions.
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%I #4 Nov 22 2018 18:18:05

%S 1,1,0,1,2,1,0,0,1,1,0,1,3,6,1,0,0,0,0,1,2,0,0,0,1,0,1,0,0,1,2,2,2,0,

%T 1,6,4,12,24,1,0,0,0,0,0,0,1,1,0,0,0,0,0,1,0,1,0,0,0,0,1,1,2,2,0,0,0,

%U 1,2,1,0,2,0,0,1,3,4,6,6,6,0,1,5,10,30

%N Tetrangle where T(n,H(u),H(v)) is the coefficient of m(v) in p(u), where u and v are integer partitions of n, H is Heinz number, m is monomial symmetric functions, and p is power sum symmetric functions.

%C The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>

%e Tetrangle begins (zeroes not shown):

%e (1): 1

%e .

%e (2): 1

%e (11): 1 2

%e .

%e (3): 1

%e (21): 1 1

%e (111): 1 3 6

%e .

%e (4): 1

%e (22): 1 2

%e (31): 1 1

%e (211): 1 2 2 2

%e (1111): 1 6 4 12 24

%e .

%e (5): 1

%e (41): 1 1

%e (32): 1 1

%e (221): 1 1 2 2

%e (311): 1 2 1 2

%e (2111): 1 3 4 6 6 6

%e (11111): 1 5 10 30 20 60 20

%e For example, row 14 gives: p(32) = m(5) + m(32).

%Y This is a regrouping of the triangle A321750.

%Y Cf. A005651, A008480, A056239, A124794, A124795, A215366, A318284, A319191, A319193, A321912-A321935.

%K nonn,tabf

%O 1,5

%A _Gus Wiseman_, Nov 22 2018