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

1,6

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 (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).

Crossrefs

This is a regrouping of the triangle A321897.

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

Sequence in context: A059087 A353493 A321932 * A030373 A079343 A004566

Adjacent sequences: A321930 A321931 A321932 * A321934 A321935 A321936

Keyword

nonn,tabf

Author

Gus Wiseman, Nov 23 2018

Status

approved