%I #4 Nov 20 2018 16:31:10
%S 1,1,-1,1,1,0,1,-2,1,-1,1,0,-1,1,2,-3,1,1,0,0,0,1,-1,0,0,1,-1,-1,1,0,
%T 1,-2,-2,3,3,-4,1,-1,0,1,0,0,-1,2,2,1,-1,-3,-6,6,4,-5,1,-1,1,2,-2,-1,
%U 1,0,0,1,-1,1,-1,0,0,1,0,0,0,0,1,-2,-2,-2,6,3,3
%N Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of e(v) in s(u), where H is Heinz number, e is elementary symmetric functions, and s is Schur 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).
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e Triangle begins:
%e 1
%e 1
%e -1 1
%e 1 0
%e 1 -2 1
%e -1 1 0
%e -1 1 2 -3 1
%e 1 0 0
%e 0 1 -1 0 0
%e 1 -1 -1 1 0
%e 1 -2 -2 3 3 -4 1
%e -1 0 1 0 0
%e -1 2 2 1 -1 -3 -6 6 4 -5 1
%e -1 1 2 -2 -1 1 0
%e 0 1 -1 1 -1 0 0
%e 1 0 0 0 0
%e 1 -2 -2 -2 6 3 3 3 -4 -4 -12 10 5 -6 1
%e 0 -1 1 0 0 0 0
%e For example, row 14 gives: s(41) = -e(5) + 2e(32) + e(41) - 2e(221) - e(311) + e(2111).
%Y Row sums are A036987.
%Y Cf. A000085, A008480, A056239, A082733, A124795, A153452, A296188, A300121, A304438, A317552, A317554, A321742-A321765.
%K sign,tabf
%O 1,8
%A _Gus Wiseman_, Nov 20 2018