%I #5 Nov 20 2018 19:46:26
%S 1,1,-1,0,1,1,1,0,0,-2,-1,0,-1,0,0,0,0,1,1,1,1,1,0,0,0,2,0,1,0,0,1,0,
%T 0,0,0,0,0,-3,-2,-2,-1,0,-1,0,0,0,0,0,0,0,0,0,0,-2,-1,0,0,0,0,0,-2,0,
%U -1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0
%N Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of m(v) in f(u), where H is Heinz number, m is monomial symmetric functions, and f is forgotten symmetric functions.
%C Row n has length A000041(A056239(n)).
%C The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%C a(n) is also the coefficient of f(v) in m(u).
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e Triangle begins:
%e 1
%e 1
%e -1 0
%e 1 1
%e 1 0 0
%e -2 -1 0
%e -1 0 0 0 0
%e 1 1 1
%e 1 1 0 0 0
%e 2 0 1 0 0
%e 1 0 0 0 0 0 0
%e -3 -2 -2 -1 0
%e -1 0 0 0 0 0 0 0 0 0 0
%e -2 -1 0 0 0 0 0
%e -2 0 -1 0 0 0 0
%e 1 1 1 1 1
%e 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e 3 1 2 1 0 0 0
%e For example, row 12 gives: f(211) = -3m(4) - 2m(22) - 2m(31) - m(211).
%Y Row sums are A321887.
%Y Cf. A005651, A008277, A008480, A048994, A056239, A124794, A124795, A135278, A300121, A319193, A321742-A321765.
%K sign,tabf
%O 1,10
%A _Gus Wiseman_, Nov 20 2018