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%I #6 Nov 20 2018 16:30:23
%S 1,1,-1,1,0,1,1,-2,1,0,-1,1,-1,1,2,-3,1,0,0,1,0,1,0,-2,1,0,0,1,-2,1,1,
%T -2,-2,3,3,-4,1,0,0,0,-1,1,-1,2,2,1,-1,-3,-6,6,4,-5,1,0,-1,0,1,2,-3,1,
%U 0,0,-1,2,1,-3,1,0,0,0,0,1,1,-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 h(u) or, equivalently, the coefficient of h(v) in e(u), where H is Heinz number, e is elementary symmetric functions, and h is homogeneous 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).
%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 0 1
%e 1 -2 1
%e 0 -1 1
%e -1 1 2 -3 1
%e 0 0 1
%e 0 1 0 -2 1
%e 0 0 1 -2 1
%e 1 -2 -2 3 3 -4 1
%e 0 0 0 -1 1
%e -1 2 2 1 -1 -3 -6 6 4 -5 1
%e 0 -1 0 1 2 -3 1
%e 0 0 -1 2 1 -3 1
%e 0 0 0 0 1
%e 1 -2 -2 -2 6 3 3 3 -4 -4 -12 10 5 -6 1
%e 0 0 0 1 0 -2 1
%e For example, row 14 gives: h(41) = -e(41) + e(221) + 2e(311) - 3e(2111) + e(11111).
%Y Row sums are A036987.
%Y Cf. A005651, A008480, A048994, A056239, A124794, A124795, A135278, A319191, A319193, A321742-A321765.
%K sign,tabf
%O 1,8
%A _Gus Wiseman_, Nov 20 2018
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