A321927 - OEIS

%I #4 Nov 23 2018 07:59:40

%S 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 -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 2,1,0,0,0,3,2,1,0,1,0,0,-4,-3,-3,-2,-2,-1,0

%N 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 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

%C Also the coefficient of f(v) in m(u).

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>

%e Tetrangle begins (zeroes not shown):

%e   (1):  1

%e .

%e   (2):  -1

%e   (11):  1  1

%e .

%e   (3):    1

%e   (21):  -2 -1

%e   (111):  1  1  1

%e .

%e   (4):    -1

%e   (22):    1  1

%e   (31):    2     1

%e   (211):  -3 -2 -2 -1

%e   (1111):  1  1  1  1  1

%e .

%e   (5):      1

%e   (41):    -2 -1

%e   (32):    -2    -1

%e   (221):    3  1  2  1

%e   (311):    3  2  1     1

%e   (2111):  -4 -3 -3 -2 -2 -1

%e   (11111):  1  1  1  1  1  1  1

%e For example, row 14 gives: f(32) = -2m(5) - m(32).

%Y This is a regrouping of the triangle A321886.

%Y Cf. A005651, A008480, A056239, A124794, A124795, A215366, A318284, A318360, A319191, A319193, A321912-A321935.

%K sign,tabf

%O 1,9

%A _Gus Wiseman_, Nov 22 2018