A321918 Tetrangle where T(n,H(u),H(v)) is the coefficient of e(v) in p(u), where u and v are integer partitions of n, H is Heinz number, e is elementary symmetric functions, and p is power sum symmetric functions.

1, -2, 1, 0, 1, 3, -3, 1, 0, -2, 1, 0, 0, 1, -4, 2, 4, -4, 1, 0, 4, 0, -4, 1, 0, 0, 3, -3, 1, 0, 0, 0, -2, 1, 0, 0, 0, 0, 1, 5, -5, -5, 5, 5, -5, 1, 0, -4, 0, 2, 4, -4, 1, 0, 0, -6, 6, 3, -5, 1, 0, 0, 0, 4, 0, -4, 1, 0, 0, 0, 0, 3, -3, 1, 0, 0, 0, 0, 0, -2, 1

Offset

1,2

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..81.

Wikipedia, Symmetric polynomial

Example

Tetrangle begins (zeroes not shown):
  (1):  1
.
  (2):  -2  1
  (11):     1
.
  (3):    3 -3  1
  (21):     -2  1
  (111):        1
.
  (4):    -4  2  4 -4  1
  (22):       4    -4  1
  (31):          3 -3  1
  (211):           -2  1
  (1111):              1
.
  (5):      5 -5 -5  5  5 -5  1
  (41):       -4     2  4 -4  1
  (32):          -6  6  3 -5  1
  (221):             4    -4  1
  (311):                3 -3  1
  (2111):                 -2  1
  (11111):                    1
For example, row 14 gives: p(32) = -6e(32) + 6e(221) + 3e(311) - 5e(2111) + e(11111).

Crossrefs

This is a regrouping of the triangle A321752.

Cf. A005651, A008480, A056239, A124794, A124795, A135278, A215366, A318284, A319191, A319193, A319225, A319226, A321912-A321935.

Sequence in context: A274581 A353279 A321919 * A321754 A321752 A349839

Adjacent sequences: A321915 A321916 A321917 * A321919 A321920 A321921

Keyword

sign,tabf

Author

Gus Wiseman, Nov 22 2018

Status

approved