A321924 Tetrangle where T(n,H(u),H(v)) is the coefficient of m(v) in s(u), where u and v are integer partitions of n, H is Heinz number, m is monomial symmetric functions, and s is Schur functions.

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

Offset

1,11

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..87.

Wikipedia, Symmetric polynomial

Example

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

Crossrefs

This is a regrouping of the triangle A321761.

Cf. A005651, A008480, A056239, A124794, A124795, A153452, A215366, A296188, A300121, A319191, A319193, A321912-A321935.

Sequence in context: A140698 A231599 A333290 * A124764 A151899 A268374

Adjacent sequences: A321921 A321922 A321923 * A321925 A321926 A321927

Keyword

nonn,tabf

Author

Gus Wiseman, Nov 22 2018

Status

approved