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).

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

Author

Gus Wiseman, Sep 14 2018

Keywords

• nonn
• tabf

Comments

Is this sequence nonnegative? If so, is there a combinatorial interpretation?

Examples

			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.

Cf. A056239, A093641, A153452, A153734, A215366, A296188, A296561, A299699, A305940, A317554.