A321900 - OEIS

A321900

Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of p(v) in S(u), where H is Heinz number, p is power sum symmetric functions, and S is augmented Schur functions.

1, 1, 1, 1, -1, 1, 2, 3, 1, -1, 0, 1, 6, 3, 8, 6, 1, 2, -3, 1, 0, 3, -4, 0, 1, -2, -1, 0, 2, 1, 24, 30, 20, 15, 20, 10, 1, 2, -1, 0, -2, 1, 120, 90, 144, 40, 15, 90, 120, 45, 40, 15, 1, -6, 0, -5, 0, 5, 5, 1, 0, -6, 4, 3, -4, 2, 1, -6, 3, 8, -6, 1, 720, 840

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OFFSET

1,7

COMMENTS

Row n has length A000041(A056239(n)).

The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

We define the augmented Schur functions to be S(y) = |y|! * s(y) / syt(y), where s is Schur functions and syt(y) is the number of standard Young tableaux of shape y.

LINKS

Table of n, a(n) for n=1..74.

Wikipedia, Symmetric polynomial

EXAMPLE

Triangle begins:

1 1

-1 1

2 3 1

-1 0 1

6 3 8 6 1

2 -3 1

0 3 -4 0 1