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A321928 Tetrangle where T(n,H(u),H(v)) is the coefficient of f(v) in p(u), where u and v are integer partitions of n, H is Heinz number, f is forgotten symmetric functions, and p is power sum symmetric functions.

%I A321928 #4 Nov 23 2018 07:59:48
%S A321928 1,-1,0,1,2,1,0,0,-1,-1,0,1,3,6,-1,0,0,0,0,1,2,0,0,0,1,0,1,0,0,-1,-2,
%T A321928 -2,-2,0,1,6,4,12,24,1,0,0,0,0,0,0,-1,-1,0,0,0,0,0,-1,0,-1,0,0,0,0,1,
%U A321928 1,2,2,0,0,0,1,2,1,0,2,0,0,-1,-3,-4,-6,-6,-6
%N A321928 Tetrangle where T(n,H(u),H(v)) is the coefficient of f(v) in p(u), where u and v are integer partitions of n, H is Heinz number, f is forgotten symmetric functions, and p is power sum symmetric functions.
%C A321928 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A321928 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e A321928 Tetrangle begins (zeroes not shown):
%e A321928   (1):  1
%e A321928 .
%e A321928   (2):  -1
%e A321928   (11):  1  2
%e A321928 .
%e A321928   (3):    1
%e A321928   (21):  -1 -1
%e A321928   (111):  1  3  6
%e A321928 .
%e A321928   (4):    -1
%e A321928   (22):    1  2
%e A321928   (31):    1     1
%e A321928   (211):  -1 -2 -2 -2
%e A321928   (1111):  1  6  4 12 24
%e A321928 .
%e A321928   (5):      1
%e A321928   (41):    -1 -1
%e A321928   (32):    -1    -1
%e A321928   (221):    1  1  2  2
%e A321928   (311):    1  2  1     2
%e A321928   (2111):  -1 -3 -4 -6 -6 -6
%e A321928   (11111):  1  5 10 30 20 60 20
%e A321928 For example, row 14 gives: p(32) = -f(5) - f(32).
%Y A321928 An unsigned version is A321917. This is a regrouping of the triangle A321888.
%Y A321928 Cf. A005651, A008480, A056239, A124794, A124795, A215366, A318284, A318360, A319191, A319193, A321912-A321935.
%K A321928 sign,tabf
%O A321928 1,5
%A A321928 _Gus Wiseman_, Nov 22 2018