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A321931 Tetrangle where T(n,H(u),H(v)) is the coefficient of p(v) in M(u), where u and v are integer partitions of n, H is Heinz number, p is power sum symmetric functions, and M is augmented monomial symmetric functions. 4
1, 1, 0, -1, 1, 1, 0, 0, -1, 1, 0, 2, -3, 1, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 1, 0, 0, 2, -1, -2, 1, 0, -6, 3, 8, -6, 1, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 2, -1, -2, 1, 0, 0, 0, 2, -2, -1, 0, 1, 0, 0, -6, 6, 5, -3, -3, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,12

COMMENTS

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

The augmented monomial symmetric functions are given by M(y) = c(y) * m(y) where c(y) = Product_i (y)_i! where (y)_i is the number of i's in y and m is monomial symmetric functions.

LINKS

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

Wikipedia, Symmetric polynomial

EXAMPLE

Tetrangle begins (zeros not shown):

  (1):  1

.

  (2):   1

  (11): -1  1

.

  (3):    1

  (21):  -1  1

  (111):  2 -3  1

.

  (4):     1

  (22):   -1  1

  (31):   -1     1

  (211):   2 -1 -2  1

  (1111): -6  3  8 -6  1

.

  (5):      1

  (41):    -1  1

  (32):    -1     1

  (221):    2 -1 -2  1

  (311):    2 -2 -1     1

  (2111):  -6  6  5 -3 -3  1

  (11111): 24 30 20 15 20 10  1

For example, row 14 gives: M(32) = -p(5) + p(32).

CROSSREFS

Row sums are A155972. This is a regrouping of the triangle A321895.

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

Sequence in context: A175669 A288839 A286583 * A321934 A004579 A081371

Adjacent sequences:  A321928 A321929 A321930 * A321932 A321933 A321934

KEYWORD

sign,tabf

AUTHOR

Gus Wiseman, Nov 23 2018

STATUS

approved

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Last modified May 17 12:01 EDT 2021. Contains 343971 sequences. (Running on oeis4.)