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.

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

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