A321927 Tetrangle where T(n,H(u),H(v)) is the coefficient of m(v) in f(u), where u and v are integer partitions of n, H is Heinz number, m is monomial symmetric functions, and f is forgotten symmetric functions.

1, -1, 0, 1, 1, 1, 0, 0, -2, -1, 0, 1, 1, 1, -1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 1, 0, 0, -3, -2, -2, -1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 3, 1, 2, 1, 0, 0, 0, 3, 2, 1, 0, 1, 0, 0, -4, -3, -3, -2, -2, -1, 0

Offset

1,9

Comments

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

Also the coefficient of f(v) in m(u).

Links

Table of n, a(n) for n=1..81.

Wikipedia, Symmetric polynomial

Example

Tetrangle begins (zeroes not shown):
  (1):  1
.
  (2):  -1
  (11):  1  1
.
  (3):    1
  (21):  -2 -1
  (111):  1  1  1
.
  (4):    -1
  (22):    1  1
  (31):    2     1
  (211):  -3 -2 -2 -1
  (1111):  1  1  1  1  1
.
  (5):      1
  (41):    -2 -1
  (32):    -2    -1
  (221):    3  1  2  1
  (311):    3  2  1     1
  (2111):  -4 -3 -3 -2 -2 -1
  (11111):  1  1  1  1  1  1  1
For example, row 14 gives: f(32) = -2m(5) - m(32).

Crossrefs

This is a regrouping of the triangle A321886.

Cf. A005651, A008480, A056239, A124794, A124795, A215366, A318284, A318360, A319191, A319193, A321912-A321935.

Sequence in context: A065712 A153172 A242498 * A016194 A258139 A261887

Adjacent sequences: A321924 A321925 A321926 * A321928 A321929 A321930

Keyword

sign,tabf

Author

Gus Wiseman, Nov 22 2018

Status

approved