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 A321931 Tetrangle where T(n,H(u),H(v)) is the coefficient of p(v) in M(u), where u and v are integer partitions of n, H is Heinz number, p is power sum symmetric functions, and M is augmented monomial symmetric functions. 4
 1, 1, 0, -1, 1, 1, 0, 0, -1, 1, 0, 2, -3, 1, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 1, 0, 0, 2, -1, -2, 1, 0, -6, 3, 8, -6, 1, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 2, -1, -2, 1, 0, 0, 0, 2, -2, -1, 0, 1, 0, 0, -6, 6, 5, -3, -3, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,12 COMMENTS The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k). The augmented monomial symmetric functions are given by M(y) = c(y) * m(y) where c(y) = Product_i (y)_i! where (y)_i is the number of i's in y and m is monomial symmetric functions. LINKS Wikipedia, Symmetric polynomial EXAMPLE Tetrangle begins (zeros not shown):   (1):  1 .   (2):   1   (11): -1  1 .   (3):    1   (21):  -1  1   (111):  2 -3  1 .   (4):     1   (22):   -1  1   (31):   -1     1   (211):   2 -1 -2  1   (1111): -6  3  8 -6  1 .   (5):      1   (41):    -1  1   (32):    -1     1   (221):    2 -1 -2  1   (311):    2 -2 -1     1   (2111):  -6  6  5 -3 -3  1   (11111): 24 30 20 15 20 10  1 For example, row 14 gives: M(32) = -p(5) + p(32). CROSSREFS Row sums are A155972. This is a regrouping of the triangle A321895. Cf. A008480, A056239, A124794, A124795, A215366, A318284, A318360, A319191, A319193, A321912-A321935. Sequence in context: A175669 A288839 A286583 * A321934 A004579 A081371 Adjacent sequences:  A321928 A321929 A321930 * A321932 A321933 A321934 KEYWORD sign,tabf AUTHOR Gus Wiseman, Nov 23 2018 STATUS approved

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Last modified May 17 12:01 EDT 2021. Contains 343971 sequences. (Running on oeis4.)