A321921 Tetrangle where T(n,H(u),H(v)) is the coefficient of s(v) in e(u), where u and v are integer partitions of n, H is Heinz number, s is Schur functions, and e is elementary symmetric functions.

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

Offset

1,13

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
  (11): 1 1
.
  (3):       1
  (21):    1 1
  (111): 1 2 1
.
  (4):            1
  (22):     1   1 1
  (31):         1 1
  (211):    1 1 2 1
  (1111): 1 2 3 3 1
.
  (5):                 1
  (41):              1 1
  (32):          1   1 1
  (221):       1 2 1 2 1
  (311):         1 1 2 1
  (2111):    1 2 3 3 3 1
  (11111): 1 4 5 5 6 4 1
For example, row 14 gives: e(32) = s(221) + s(2111) + s(11111).

Crossrefs

This is a regrouping of the triangle A321756.

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

Sequence in context: A302721 A321740 A098082 * A236419 A114448 A068933

Adjacent sequences: A321918 A321919 A321920 * A321922 A321923 A321924

Keyword

nonn,tabf

Author

Gus Wiseman, Nov 22 2018

Status

approved