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%I #4 Nov 23 2018 07:59:18
%S 1,1,1,0,1,1,1,1,0,1,2,0,0,1,1,1,1,1,1,0,1,0,1,2,0,1,1,2,3,0,0,0,1,3,
%T 0,0,0,0,1,1,1,1,1,1,1,1,0,1,1,2,2,3,4,0,0,1,2,1,3,5,0,0,0,1,0,2,5,0,
%U 0,0,1,1,3,6,0,0,0,0,0,1,4,0,0,0,0,0,0
%N Tetrangle where T(n,H(u),H(v)) is the coefficient of m(v) in s(u), where u and v are integer partitions of n, H is Heinz number, m is monomial symmetric functions, and s is Schur 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 1
%e (11): 1
%e .
%e (3): 1 1 1
%e (21): 1 2
%e (111): 1
%e .
%e (4): 1 1 1 1 1
%e (22): 1 1 2
%e (31): 1 1 2 3
%e (211): 1 3
%e (1111): 1
%e .
%e (5): 1 1 1 1 1 1 1
%e (41): 1 1 2 2 3 4
%e (32): 1 2 1 3 5
%e (221): 1 2 5
%e (311): 1 1 3 6
%e (2111): 1 4
%e (11111): 1
%e For example, row 14 gives: s(32) = m(32) + 2m(221) + m(311) + 3m(2111) + 5m(11111).
%Y This is a regrouping of the triangle A321761.
%Y Cf. A005651, A008480, A056239, A124794, A124795, A153452, A215366, A296188, A300121, A319191, A319193, A321912-A321935.
%K nonn,tabf
%O 1,11
%A _Gus Wiseman_, Nov 22 2018