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A321914 Tetrangle where T(n,H(u),H(v)) is the coefficient of e(v) in m(u), where u and v are integer partitions of n, H is Heinz number, m is monomial symmetric functions, and e is elementary symmetric functions.

%I A321914 #4 Nov 22 2018 18:17:44
%S A321914 1,-2,1,1,0,3,-3,1,-3,1,0,1,0,0,-4,2,4,-4,1,2,1,-2,0,0,4,-2,-1,1,0,-4,
%T A321914 0,1,0,0,1,0,0,0,0,5,-5,-5,5,5,-5,1,-5,1,5,-3,-1,1,0,-5,5,-1,1,-2,0,0,
%U A321914 5,-3,1,0,0,0,0,5,-1,-2,0,1,0,0,-5,1,0,0,0,0
%N A321914 Tetrangle where T(n,H(u),H(v)) is the coefficient of e(v) in m(u), where u and v are integer partitions of n, H is Heinz number, m is monomial symmetric functions, and e is elementary symmetric functions.
%C A321914 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%C A321914 Also the coefficient of h(v) in f(u), where f is forgotten symmetric functions and h is homogeneous symmetric functions.
%H A321914 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e A321914 Tetrangle begins (zeroes not shown):
%e A321914   (1):  1
%e A321914 .
%e A321914   (2):  -2  1
%e A321914   (11):  1
%e A321914 .
%e A321914   (3):    3 -3  1
%e A321914   (21):  -3  1
%e A321914   (111):  1
%e A321914 .
%e A321914   (4):    -4  2  4 -4  1
%e A321914   (22):    2  1 -2
%e A321914   (31):    4 -2 -1  1
%e A321914   (211):  -4     1
%e A321914   (1111):  1
%e A321914 .
%e A321914   (5):      5 -5 -5  5  5 -5  1
%e A321914   (41):    -5  1  5 -3 -1  1
%e A321914   (32):    -5  5 -1  1 -2
%e A321914   (221):    5 -3  1
%e A321914   (311):    5 -1 -2     1
%e A321914   (2111):  -5  1
%e A321914   (11111):  1
%e A321914 For example, row 14 gives: m(32) = -5e(5) - e(32) + 5e(41) + e(221) - 2e(311).
%Y A321914 This is a regrouping of the triangle A321746.
%Y A321914 Cf. A005651, A008480, A056239, A124794, A124795, A215366, A318284, A318360, A319191, A319193, A321854, A321738, A321912-A321935.
%K A321914 sign,tabf
%O A321914 1,2
%A A321914 _Gus Wiseman_, Nov 22 2018