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A321926 Tetrangle where T(n,H(u),H(v)) is the coefficient of s(v) in p(u), where u and v are integer partitions of n, H is Heinz number, s is Schur functions, and p is power sum symmetric functions.

%I A321926 #4 Nov 23 2018 07:59:33
%S A321926 1,1,-1,1,1,1,-1,1,1,0,-1,1,2,1,1,0,-1,1,-1,1,2,-1,-1,1,1,-1,0,0,1,1,
%T A321926 0,1,-1,-1,1,2,3,3,1,1,-1,0,0,1,-1,1,1,0,-1,1,0,0,-1,1,-1,1,-1,0,1,-1,
%U A321926 1,0,1,1,-2,0,1,1,1,-1,-1,0,1,1,1,2,1,-1,0,-2
%N A321926 Tetrangle where T(n,H(u),H(v)) is the coefficient of s(v) in p(u), where u and v are integer partitions of n, H is Heinz number, s is Schur functions, and p is power sum symmetric functions.
%C A321926 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A321926 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e A321926 Tetrangle begins (zeroes not shown):
%e A321926   (1):  1
%e A321926 .
%e A321926   (2):   1 -1
%e A321926   (11):  1  1
%e A321926 .
%e A321926   (3):    1 -1  1
%e A321926   (21):   1    -1
%e A321926   (111):  1  2  1
%e A321926 .
%e A321926   (4):     1    -1  1 -1
%e A321926   (22):    1  2 -1 -1  1
%e A321926   (31):    1 -1        1
%e A321926   (211):   1     1 -1 -1
%e A321926   (1111):  1  2  3  3  1
%e A321926 .
%e A321926   (5):      1 -1        1 -1  1
%e A321926   (41):     1    -1  1       -1
%e A321926   (32):     1 -1  1 -1     1 -1
%e A321926   (221):    1     1  1 -2     1
%e A321926   (311):    1  1 -1 -1     1  1
%e A321926   (2111):   1  2  1 -1    -2 -1
%e A321926   (11111):  1  4  5  5  6  4  1
%e A321926 For example, row 14 gives: p(32) = s(5) + s(32) - s(41) - s(221) + s(2111) - s(11111).
%Y A321926 Row sums are A317552. This is a regrouping of the triangle A321765.
%Y A321926 Cf. A005651, A008480, A056239, A124794, A124795, A153452, A215366, A296188, A300121, A319191, A319193, A321912-A321935.
%K A321926 sign,tabf
%O A321926 1,13
%A A321926 _Gus Wiseman_, Nov 22 2018