A321933 - OEIS

%I #6 Nov 23 2018 21:13:57

%S 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,

%T 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,

%U 2,1,0,0,0,0,2,3,1,0,0,0,0,0,1,1,0,0,0,0

%N 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.

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>

%e Tetrangle begins (zeros not shown):

%e   (1):  1

%e .

%e   (2):   1  1

%e   (11):     1

%e .

%e   (3):    2  3  1

%e   (21):      1  1

%e   (111):        1

%e .

%e   (4):     6  3  8  6  1

%e   (22):       1     2  1

%e   (31):          2  3  1

%e   (211):            1  1

%e   (1111):              1

%e .

%e   (5):     24 30 20 15 20 10  1

%e   (41):        6     3  8  6  1

%e   (32):           2  3  2  4  1

%e   (221):             1     2  1

%e   (311):                2  3  1

%e   (2111):                  1  1

%e   (11111):                    1

%e For example, row 14 gives: 12h(32) = 2p(32) + 3p(221) + 2p(311) + 4p(2111) + p(11111).

%Y This is a regrouping of the triangle A321897.

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

%K nonn,tabf

%O 1,6

%A _Gus Wiseman_, Nov 23 2018