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%I #4 Nov 22 2018 18:17:58
%S 1,-1,1,0,1,1,-2,1,0,-1,1,0,0,1,-1,1,2,-3,1,0,1,0,-2,1,0,0,1,-2,1,0,0,
%T 0,-1,1,0,0,0,0,1,1,-2,-2,3,3,-4,1,0,-1,0,1,2,-3,1,0,0,-1,2,1,-3,1,0,
%U 0,0,1,0,-2,1,0,0,0,0,1,-2,1,0,0,0,0,0,-1,1
%N Tetrangle where T(n,H(u),H(v)) is the coefficient of e(v) in h(u), where u and v are integer partitions of n, H is Heinz number, e is elementary symmetric functions, and h is homogeneous symmetric functions.
%C The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%C Also the coefficient of h(v) in e(u).
%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 -2 1
%e (21): -1 1
%e (111): 1
%e .
%e (4): -1 1 2 -3 1
%e (22): 1 -2 1
%e (31): 1 -2 1
%e (211): -1 1
%e (1111): 1
%e .
%e (5): 1 -2 -2 3 3 -4 1
%e (41): -1 1 2 -3 1
%e (32): -1 2 1 -3 1
%e (221): 1 -2 1
%e (311): 1 -2 1
%e (2111): -1 1
%e (11111): 1
%e For example, row 14 gives: h(32) = -e(32) + 2e(221) + e(311) - 3e(2111) + e(11111).
%Y This is a regrouping of the triangle A321749. Row sums are A134286.
%Y Cf. A005651, A008480, A056239, A124794, A124795, A215366, A318284, A318360, A319191, A319193, A321912-A321935.
%K sign,tabf
%O 1,7
%A _Gus Wiseman_, Nov 22 2018
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