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 A321923 Tetrangle where T(n,H(u),H(v)) is the coefficient of s(v) in h(u), where u and v are integer partitions of n, H is Heinz number, s is Schur functions, and h is homogeneous symmetric functions. 0
 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 2, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 2, 1, 0, 1, 2, 3, 3, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 2, 1, 1, 0, 0, 1, 2, 1, 0, 1, 0, 0, 1, 3, 3, 2, 3, 1, 0, 1, 4, 5, 5, 6, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,13 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..87. Wikipedia, Symmetric polynomial EXAMPLE Tetrangle begins (zeroes not shown): (1): 1 . (2): 1 (11): 1 1 . (3): 1 (21): 1 1 (111): 1 2 1 . (4): 1 (22): 1 1 1 (31): 1 1 (211): 1 1 2 1 (1111): 1 2 3 3 1 . (5): 1 (41): 1 1 (32): 1 1 1 (221): 1 2 2 1 1 (311): 1 2 1 1 (2111): 1 3 3 2 3 1 (11111): 1 4 5 5 6 4 1 For example, row 14 gives: h(32) = s(5) + s(32) + s(41). CROSSREFS This is a regrouping of the triangle A321759. Cf. A005651, A008480, A056239, A124794, A124795, A153452, A215366, A296188, A300121, A319191, A319193, A321912-A321935. Sequence in context: A175134 A027355 A127326 * A064663 A025923 A351358 Adjacent sequences: A321920 A321921 A321922 * A321924 A321925 A321926 KEYWORD nonn,tabf AUTHOR Gus Wiseman, Nov 22 2018 STATUS approved

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Last modified March 5 10:18 EST 2024. Contains 370548 sequences. (Running on oeis4.)