%I #4 Nov 22 2018 18:17:38
%S 1,1,1,1,2,1,1,1,1,2,3,1,3,6,1,1,1,1,1,1,3,2,4,6,1,2,2,3,4,1,4,3,7,12,
%T 1,6,4,12,24,1,1,1,1,1,1,1,1,2,2,3,3,4,5,1,2,3,5,4,7,10,1,3,5,11,8,18,
%U 30,1,3,4,8,7,13,20,1,4,7,18,13,33,60,1,5
%N Tetrangle where T(n,H(u),H(v)) is the coefficient of m(v) in h(u), where u and v are integer partitions of n, H is Heinz number, m is monomial 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).
%C Also the coefficient of f(v) in e(u), where f is forgotten symmetric functions and e is elementary symmetric functions.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e Tetrangle begins:
%e (1): 1
%e .
%e (2): 1 1
%e (11): 1 2
%e .
%e (3): 1 1 1
%e (21): 1 2 3
%e (111): 1 3 6
%e .
%e (4): 1 1 1 1 1
%e (22): 1 3 2 4 6
%e (31): 1 2 2 3 4
%e (211): 1 4 3 7 12
%e (1111): 1 6 4 12 24
%e .
%e (5): 1 1 1 1 1 1 1
%e (41): 1 2 2 3 3 4 5
%e (32): 1 2 3 5 4 7 10
%e (221): 1 3 5 11 8 18 30
%e (311): 1 3 4 8 7 13 20
%e (2111): 1 4 7 18 13 33 60
%e (11111): 1 5 10 30 20 60 20
%e For example, row 14 gives: h(32) = m(5) + 3m(32) + 2m(41) + 5m(221) + 4m(311) + 7m(2111) + 10m(11111).
%Y This is a regrouping of the triangle A321744.
%Y Cf. A005651, A008480, A056239, A124794, A124795, A215366, A318284, A319191, A319193, A321912-A321935.
%K nonn,tabf
%O 1,5
%A _Gus Wiseman_, Nov 22 2018