A321886 -id:A321886 - cp's OEIS frontend

A321887 Sum of coefficients of monomial symmetric functions in the forgotten symmetric function of the integer partition with Heinz number n.

1, 1, -1, 2, 1, -3, -1, 3, 2, 3, 1, -8, -1, -3, -3, 5, 1, 7, -1, 7, 3, 3, 1, -15

Offset: 1

Gus Wiseman, Nov 20 2018

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

			The sum of coefficients of m(221) = 3m(5) + 2m(32) + m(41) + m(221) is a(18) = 7.

Wikipedia, Symmetric polynomial

Row sums of A321886.

Cf. A005651, A008277, A008480, A056239, A124794, A124795, A296150, A319182, A319193, A321742-A321765.

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.

Original entry on oeis.org

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

Gus Wiseman, Nov 22 2018

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).

			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).

Wikipedia, Symmetric polynomial

This is a regrouping of the triangle A321886.

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

cp's OEIS Frontend

A321887 Sum of coefficients of monomial symmetric functions in the forgotten symmetric function of the integer partition with Heinz number n.

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