A321928 Tetrangle where T(n,H(u),H(v)) is the coefficient of f(v) in p(u), where u and v are integer partitions of n, H is Heinz number, f is forgotten symmetric functions, and p is power sum symmetric functions.
1, -1, 0, 1, 2, 1, 0, 0, -1, -1, 0, 1, 3, 6, -1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 1, 0, 1, 0, 0, -1, -2, -2, -2, 0, 1, 6, 4, 12, 24, 1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 1, 1, 2, 2, 0, 0, 0, 1, 2, 1, 0, 2, 0, 0, -1, -3, -4, -6, -6, -6
Offset: 1
Examples
Tetrangle begins (zeroes not shown): (1): 1 . (2): -1 (11): 1 2 . (3): 1 (21): -1 -1 (111): 1 3 6 . (4): -1 (22): 1 2 (31): 1 1 (211): -1 -2 -2 -2 (1111): 1 6 4 12 24 . (5): 1 (41): -1 -1 (32): -1 -1 (221): 1 1 2 2 (311): 1 2 1 2 (2111): -1 -3 -4 -6 -6 -6 (11111): 1 5 10 30 20 60 20 For example, row 14 gives: p(32) = -f(5) - f(32).
Links
- Wikipedia, Symmetric polynomial
Comments