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A321927 Tetrangle where T(n,H(u),H(v)) is the coefficient of m(v) in f(u), where u and v are integer partitions of n, H is Heinz number, m is monomial symmetric functions, and f is forgotten symmetric functions.

%I A321927 #4 Nov 23 2018 07:59:40
%S A321927 1,-1,0,1,1,1,0,0,-2,-1,0,1,1,1,-1,0,0,0,0,1,1,0,0,0,2,0,1,0,0,-3,-2,
%T A321927 -2,-1,0,1,1,1,1,1,1,0,0,0,0,0,0,-2,-1,0,0,0,0,0,-2,0,-1,0,0,0,0,3,1,
%U A321927 2,1,0,0,0,3,2,1,0,1,0,0,-4,-3,-3,-2,-2,-1,0
%N A321927 Tetrangle where T(n,H(u),H(v)) is the coefficient of m(v) in f(u), where u and v are integer partitions of n, H is Heinz number, m is monomial symmetric functions, and f is forgotten symmetric functions.
%C A321927 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%C A321927 Also the coefficient of f(v) in m(u).
%H A321927 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e A321927 Tetrangle begins (zeroes not shown):
%e A321927   (1):  1
%e A321927 .
%e A321927   (2):  -1
%e A321927   (11):  1  1
%e A321927 .
%e A321927   (3):    1
%e A321927   (21):  -2 -1
%e A321927   (111):  1  1  1
%e A321927 .
%e A321927   (4):    -1
%e A321927   (22):    1  1
%e A321927   (31):    2     1
%e A321927   (211):  -3 -2 -2 -1
%e A321927   (1111):  1  1  1  1  1
%e A321927 .
%e A321927   (5):      1
%e A321927   (41):    -2 -1
%e A321927   (32):    -2    -1
%e A321927   (221):    3  1  2  1
%e A321927   (311):    3  2  1     1
%e A321927   (2111):  -4 -3 -3 -2 -2 -1
%e A321927   (11111):  1  1  1  1  1  1  1
%e A321927 For example, row 14 gives: f(32) = -2m(5) - m(32).
%Y A321927 This is a regrouping of the triangle A321886.
%Y A321927 Cf. A005651, A008480, A056239, A124794, A124795, A215366, A318284, A318360, A319191, A319193, A321912-A321935.
%K A321927 sign,tabf
%O A321927 1,9
%A A321927 _Gus Wiseman_, Nov 22 2018