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A321930 Tetrangle where T(n,H(u),H(v)) is the coefficient of s(v) in f(u), where u and v are integer partitions of n, H is Heinz number, f is forgotten symmetric functions, and s is Schur functions. 0
1, -1, 1, 1, 0, 1, -1, 1, -2, 1, 0, 1, 0, 0, -1, 0, 1, -1, 1, 1, 1, -1, 0, 0, 2, -1, -1, 1, 0, -3, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, -1, 0, 0, 1, -1, 1, -2, 1, 1, -1, -1, 1, 0, -2, 2, -1, 1, -1, 0, 0, 3, -2, 1, 0, 0, 0, 0, 3, -1, -1, 0, 1, 0, 0, -4, 1, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

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..80.

Wikipedia, Symmetric polynomial

EXAMPLE

Tetrangle begins (zeros not shown):

  (1):  1

.

  (2):  -1  1

  (11):  1

.

  (3):    1 -1  1

  (21):  -2  1

  (111):  1

.

  (4):    -1     1 -1  1

  (22):    1  1 -1

  (31):    2 -1 -1  1

  (211):  -3     1

  (1111):  1

.

  (5):      1 -1        1 -1  1

  (41):    -2  1  1 -1 -1  1

  (32):    -2  2 -1  1 -1

  (221):    3 -2  1

  (311):    3 -1 -1     1

  (2111):  -4  1

  (11111):  1

For example, row 14 gives: f(32) = -2s(5) - s(32) + 2s(41) + s(221) - s(311).

CROSSREFS

This is a regrouping of the triangle A321894.

Cf. A008480, A056239, A124794, A124795, A153452, A215366, A296188, A300121, A319191, A319193, A321912-A321935.

Sequence in context: A073423 A219180 A179952 * A134023 A257931 A325699

Adjacent sequences:  A321927 A321928 A321929 * A321931 A321932 A321933

KEYWORD

sign,tabf

AUTHOR

Gus Wiseman, Nov 23 2018

STATUS

approved

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Last modified July 27 10:44 EDT 2021. Contains 346304 sequences. (Running on oeis4.)