A321933 Tetrangle where T(n,H(u),H(v)) is the coefficient of p(v) in h(u) * Product_i u_i!, where u and v are integer partitions of n, H is Heinz number, p is power sum symmetric functions, and h is homogeneous symmetric functions.

1, 1, 1, 0, 1, 2, 3, 1, 0, 1, 1, 0, 0, 1, 6, 3, 8, 6, 1, 0, 1, 0, 2, 1, 0, 0, 2, 3, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 24, 30, 20, 15, 20, 10, 1, 0, 6, 0, 3, 8, 6, 1, 0, 0, 2, 3, 2, 4, 1, 0, 0, 0, 1, 0, 2, 1, 0, 0, 0, 0, 2, 3, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0

Offset: 1

Author

Gus Wiseman, Nov 23 2018

Keywords

• nonn
• tabf

Comments

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

Examples

			Tetrangle begins (zeros not shown):
  (1):  1
.
  (2):   1  1
  (11):     1
.
  (3):    2  3  1
  (21):      1  1
  (111):        1
.
  (4):     6  3  8  6  1
  (22):       1     2  1
  (31):          2  3  1
  (211):            1  1
  (1111):              1
.
  (5):     24 30 20 15 20 10  1
  (41):        6     3  8  6  1
  (32):           2  3  2  4  1
  (221):             1     2  1
  (311):                2  3  1
  (2111):                  1  1
  (11111):                    1
For example, row 14 gives: 12h(32) = 2p(32) + 3p(221) + 2p(311) + 4p(2111) + p(11111).
		

Links

• Wikipedia, Symmetric polynomial

Crossrefs

This is a regrouping of the triangle A321897.

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