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A317552
Irregular triangle where T(n,k) is the sum of coefficients in the expansion of p(y) in terms of Schur functions, where p is power-sum symmetric functions and y is the integer partition with Heinz number A215366(n,k).
14
1, 0, 2, 1, 0, 4, 0, 2, 1, 0, 10, 1, 0, 0, 2, 2, 0, 26, 0, 0, 1, 4, 0, 0, 0, 4, 4, 0, 76, 1, 0, 0, 0, 0, 2, 2, 4, 0, 0, 0, 8, 10, 0, 232, 0, 1, 0, 4, 0, 1, 0, 0, 0, 0, 12, 0, 4, 2, 8, 0, 0, 0, 20, 26, 0, 764, 1, 0, 0, 0, 2, 0, 0, 4, 2, 0, 0, 1, 10, 0, 0, 0, 0
OFFSET
1,3
COMMENTS
Is this sequence nonnegative? If so, is there a combinatorial interpretation?
EXAMPLE
Triangle begins:
1
0 2
1 0 4
0 2 1 0 10
1 0 0 2 2 0 26
0 0 1 4 0 0 0 4 4 0 76
1 0 0 0 0 2 2 4 0 0 0 8 10 0 232
A215366(6,4) = 25 corresponds to the partition (33). Since p(33) = s(6) + 2 s(33) - s(51) + 2 s(222) - 2 s(321) + s(411) + s(3111) - s(21111) + s(111111) has sum of coefficients 1 + 2 - 1 + 2 - 2 + 1 + 1 - 1 + 1 = 4, we conclude T(6,4) = 4.
CROSSREFS
Last column is A000085. Row sums are A082733.
Sequence in context: A143424 A130125 A336517 * A214809 A363902 A137336
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Sep 14 2018
STATUS
approved