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A321925 Tetrangle where T(n,H(u),H(v)) is the coefficient of s(v) in m(u), where u and v are integer partitions of n, H is Heinz number, s is Schur functions, and m is monomial symmetric functions.

%I A321925 #4 Nov 23 2018 07:59:26
%S A321925 1,1,-1,0,1,1,-1,1,0,1,-2,0,0,1,1,0,-1,1,-1,0,1,0,-1,1,0,-1,1,-1,2,0,
%T A321925 0,0,1,-3,0,0,0,0,1,1,-1,0,0,1,-1,1,0,1,-1,1,-1,1,-2,0,0,1,-1,-1,2,-2,
%U A321925 0,0,0,1,0,-2,3,0,0,0,-1,1,-1,3,0,0,0,0,0,1
%N A321925 Tetrangle where T(n,H(u),H(v)) is the coefficient of s(v) in m(u), where u and v are integer partitions of n, H is Heinz number, s is Schur functions, and m is monomial symmetric functions.
%C A321925 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A321925 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e A321925 Tetrangle begins (zeroes not shown):
%e A321925   (1):  1
%e A321925 .
%e A321925   (2):   1 -1
%e A321925   (11):     1
%e A321925 .
%e A321925   (3):    1 -1  1
%e A321925   (21):      1 -2
%e A321925   (111):        1
%e A321925 .
%e A321925   (4):     1    -1  1 -1
%e A321925   (22):       1    -1  1
%e A321925   (31):      -1  1 -1  2
%e A321925   (211):            1 -3
%e A321925   (1111):              1
%e A321925 .
%e A321925   (5):      1 -1        1 -1  1
%e A321925   (41):        1 -1  1 -1  1 -2
%e A321925   (32):           1 -1 -1  2 -2
%e A321925   (221):             1    -2  3
%e A321925   (311):            -1  1 -1  3
%e A321925   (2111):                  1 -4
%e A321925   (11111):                    1
%e A321925 For example, row 14 gives: m(32) = s(32) - s(221) - s(311) + 2s(2111) - 2s(11111).
%Y A321925 This is a regrouping of the triangle A321763.
%Y A321925 Cf. A005651, A008480, A056239, A124794, A124795, A153452, A215366, A296188, A300121, A319191, A319193, A321912-A321935.
%K A321925 sign,tabf
%O A321925 1,11
%A A321925 _Gus Wiseman_, Nov 22 2018