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Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of s(v) in p(u), where H is Heinz number, p is power sum symmetric functions, and s is Schur functions.
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%I #4 Nov 20 2018 19:46:19

%S 1,1,1,-1,1,1,1,-1,1,1,0,-1,1,0,-1,1,-1,1,2,1,1,2,-1,-1,1,1,-1,0,0,1,

%T 1,-1,0,0,1,-1,1,1,0,1,-1,-1,1,0,-1,0,0,1,0,0,-1,1,-1,1,0,-1,1,0,0,-1

%N Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of s(v) in p(u), where H is Heinz number, p is power sum 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 1

%e 1 -1 1

%e 1 0 -1

%e 1 0 -1 1 -1

%e 1 2 1

%e 1 2 -1 -1 1

%e 1 -1 0 0 1

%e 1 -1 0 0 1 -1 1

%e 1 0 1 -1 -1

%e 1 0 -1 0 0 1 0 0 -1 1 -1

%e 1 0 -1 1 0 0 -1

%e For example, row 12 gives: p(211) = s(4) + s(31) - s(211) - s(1111).

%Y Row sums are A317554.

%Y Cf. A000085, A008480, A056239, A082733, A124795, A153452, A296188, A296561, A300121, A304438, A317552, A317554, A321742-A321765.

%K sign,tabf,more

%O 1,19

%A _Gus Wiseman_, Nov 20 2018