A321929 Tetrangle where T(n,H(u),H(v)) is the coefficient of f(v) in s(u), where u and v are integer partitions of n, H is Heinz number, f is forgotten symmetric functions, and s is Schur functions.

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

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

Crossrefs

This is a regrouping of the triangle A321892.

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

Sequence in context: A086072 A086009 A086010 * A089198 A059607 A176724

Adjacent sequences: A321926 A321927 A321928 * A321930 A321931 A321932

Keyword

nonn,tabf

Author

Gus Wiseman, Nov 23 2018

Status

approved