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 A321925 Tetrangle where T(n,H(u),H(v)) is the coefficient of s(v) in m(u), where u and v are integer partitions of n, H is Heinz number, s is Schur functions, and m is monomial symmetric functions. 1
 1, 1, -1, 0, 1, 1, -1, 1, 0, 1, -2, 0, 0, 1, 1, 0, -1, 1, -1, 0, 1, 0, -1, 1, 0, -1, 1, -1, 2, 0, 0, 0, 1, -3, 0, 0, 0, 0, 1, 1, -1, 0, 0, 1, -1, 1, 0, 1, -1, 1, -1, 1, -2, 0, 0, 1, -1, -1, 2, -2, 0, 0, 0, 1, 0, -2, 3, 0, 0, 0, -1, 1, -1, 3, 0, 0, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,11 COMMENTS The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k). LINKS Table of n, a(n) for n=1..80. Wikipedia, Symmetric polynomial EXAMPLE Tetrangle begins (zeroes not shown): (1): 1 . (2): 1 -1 (11): 1 . (3): 1 -1 1 (21): 1 -2 (111): 1 . (4): 1 -1 1 -1 (22): 1 -1 1 (31): -1 1 -1 2 (211): 1 -3 (1111): 1 . (5): 1 -1 1 -1 1 (41): 1 -1 1 -1 1 -2 (32): 1 -1 -1 2 -2 (221): 1 -2 3 (311): -1 1 -1 3 (2111): 1 -4 (11111): 1 For example, row 14 gives: m(32) = s(32) - s(221) - s(311) + 2s(2111) - 2s(11111). CROSSREFS This is a regrouping of the triangle A321763. Cf. A005651, A008480, A056239, A124794, A124795, A153452, A215366, A296188, A300121, A319191, A319193, A321912-A321935. Sequence in context: A335877 A125203 A023565 * A025922 A342322 A161369 Adjacent sequences: A321922 A321923 A321924 * A321926 A321927 A321928 KEYWORD sign,tabf AUTHOR Gus Wiseman, Nov 22 2018 STATUS approved

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Last modified March 5 03:04 EST 2024. Contains 370537 sequences. (Running on oeis4.)