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A321919 Tetrangle where T(n,H(u),H(v)) is the coefficient of h(v) in p(u), where u and v are integer partitions of n, H is Heinz number, h is homogeneous symmetric functions, and p is power sum symmetric functions.

%I A321919 #4 Nov 22 2018 18:18:20
%S A321919 1,2,-1,0,1,3,-3,1,0,2,-1,0,0,1,4,-2,-4,4,-1,0,4,0,-4,1,0,0,3,-3,1,0,
%T A321919 0,0,2,-1,0,0,0,0,1,5,-5,-5,5,5,-5,1,0,4,0,-2,-4,4,-1,0,0,6,-6,-3,5,
%U A321919 -1,0,0,0,4,0,-4,1,0,0,0,0,3,-3,1,0,0,0,0,0,2
%N A321919 Tetrangle where T(n,H(u),H(v)) is the coefficient of h(v) in p(u), where u and v are integer partitions of n, H is Heinz number, h is homogeneous symmetric functions, and p is power sum symmetric functions.
%C A321919 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A321919 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e A321919 Tetrangle begins (zeroes not shown):
%e A321919   (1):  1
%e A321919 .
%e A321919   (2):   2 -1
%e A321919   (11):     1
%e A321919 .
%e A321919   (3):    3 -3  1
%e A321919   (21):      2 -1
%e A321919   (111):        1
%e A321919 .
%e A321919   (4):     4 -2 -4  4 -1
%e A321919   (22):       4    -4  1
%e A321919   (31):          3 -3  1
%e A321919   (211):            2 -1
%e A321919   (1111):              1
%e A321919 .
%e A321919   (5):      5 -5 -5  5  5 -5  1
%e A321919   (41):        4    -2 -4  4 -1
%e A321919   (32):           6 -6 -3  5 -1
%e A321919   (221):             4    -4  1
%e A321919   (311):                3 -3  1
%e A321919   (2111):                  2 -1
%e A321919   (11111):                    1
%e A321919 For example, row 14 gives: p(32) = 6h(32) - 6h(221) - 3h(311) + 5h(2111) - h(11111).
%Y A321919 This is a regrouping of the triangle A321754.
%Y A321919 Cf. A005651, A008480, A056239, A124794, A124795, A215366, A318284, A318360, A319191, A319193, A321912-A321935.
%K A321919 sign,tabf
%O A321919 1,2
%A A321919 _Gus Wiseman_, Nov 22 2018