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%I #5 Nov 21 2018 09:24:00
%S 1,1,-1,0,1,2,1,0,0,-1,-1,0,-1,0,0,0,0,1,3,6,1,2,0,0,0,1,0,1,0,0,1,0,
%T 0,0,0,0,0,-1,-2,-2,-2,0,-1,0,0,0,0,0,0,0,0,0,0,-1,-1,0,0,0,0,0,-1,0,
%U -1,0,0,0,0,1,6,4,12,24,1,0,0,0,0,0,0,0,0,0
%N Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of f(v) in p(u), where H is Heinz number, p is power sum 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 Up to sign, a(n) is also the coefficient of m(v) in p(u), where m is monomial symmetric functions.
%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 2
%e 1 0 0
%e -1 -1 0
%e -1 0 0 0 0
%e 1 3 6
%e 1 2 0 0 0
%e 1 0 1 0 0
%e 1 0 0 0 0 0 0
%e -1 -2 -2 -2 0
%e -1 0 0 0 0 0 0 0 0 0 0
%e -1 -1 0 0 0 0 0
%e -1 0 -1 0 0 0 0
%e 1 6 4 12 24
%e 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e 1 1 2 2 0 0 0
%e For example, row 12 gives: p(211) = -f(4) - 2f(22) - 2f(31) - 2f(211).
%Y Row sums are A321889.
%Y Cf. A005651, A008277, A008480, A048994, A056239, A124794, A124795, A319182, A319193, A321742-A321765.
%K sign,tabf
%O 1,6
%A _Gus Wiseman_, Nov 20 2018
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