A321917 Tetrangle where T(n,H(u),H(v)) is the coefficient of m(v) in p(u), where u and v are integer partitions of n, H is Heinz number, m is monomial symmetric functions, and p is power sum symmetric functions.

1, 1, 0, 1, 2, 1, 0, 0, 1, 1, 0, 1, 3, 6, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 1, 0, 1, 0, 0, 1, 2, 2, 2, 0, 1, 6, 4, 12, 24, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 2, 2, 0, 0, 0, 1, 2, 1, 0, 2, 0, 0, 1, 3, 4, 6, 6, 6, 0, 1, 5, 10, 30

Offset

1,5

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..85.

Wikipedia, Symmetric polynomial

Example

Tetrangle begins (zeroes not shown):
  (1):  1
.
  (2):   1
  (11):  1  2
.
  (3):    1
  (21):   1  1
  (111):  1  3  6
.
  (4):     1
  (22):    1  2
  (31):    1     1
  (211):   1  2  2  2
  (1111):  1  6  4 12 24
.
  (5):      1
  (41):     1  1
  (32):     1     1
  (221):    1  1  2  2
  (311):    1  2  1     2
  (2111):   1  3  4  6  6  6
  (11111):  1  5 10 30 20 60 20
For example, row 14 gives: p(32) = m(5) + m(32).

Crossrefs

This is a regrouping of the triangle A321750.

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

Sequence in context: A280829 A303942 A321928 * A115201 A354100 A118229

Adjacent sequences: A321914 A321915 A321916 * A321918 A321919 A321920

Keyword

nonn,tabf

Author

Gus Wiseman, Nov 22 2018

Status

approved