%I #4 Nov 23 2018 07:59:40
%S 1,-1,0,1,1,1,0,0,-2,-1,0,1,1,1,-1,0,0,0,0,1,1,0,0,0,2,0,1,0,0,-3,-2,
%T -2,-1,0,1,1,1,1,1,1,0,0,0,0,0,0,-2,-1,0,0,0,0,0,-2,0,-1,0,0,0,0,3,1,
%U 2,1,0,0,0,3,2,1,0,1,0,0,-4,-3,-3,-2,-2,-1,0
%N Tetrangle where T(n,H(u),H(v)) is the coefficient of m(v) in f(u), where u and v are integer partitions of n, H is Heinz number, m is monomial symmetric functions, and f is forgotten 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 f(v) in m(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
%e (11): 1 1
%e .
%e (3): 1
%e (21): -2 -1
%e (111): 1 1 1
%e .
%e (4): -1
%e (22): 1 1
%e (31): 2 1
%e (211): -3 -2 -2 -1
%e (1111): 1 1 1 1 1
%e .
%e (5): 1
%e (41): -2 -1
%e (32): -2 -1
%e (221): 3 1 2 1
%e (311): 3 2 1 1
%e (2111): -4 -3 -3 -2 -2 -1
%e (11111): 1 1 1 1 1 1 1
%e For example, row 14 gives: f(32) = -2m(5) - m(32).
%Y This is a regrouping of the triangle A321886.
%Y Cf. A005651, A008480, A056239, A124794, A124795, A215366, A318284, A318360, A319191, A319193, A321912-A321935.
%K sign,tabf
%O 1,9
%A _Gus Wiseman_, Nov 22 2018