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A321929 Tetrangle where T(n,H(u),H(v)) is the coefficient of f(v) in s(u), where u and v are integer partitions of n, H is Heinz number, f is forgotten symmetric functions, and s is Schur functions.

%I A321929 #6 Nov 23 2018 21:13:17
%S A321929 1,0,1,1,1,0,0,1,0,1,2,1,1,1,0,0,0,0,1,0,1,0,1,2,0,0,0,1,3,0,1,1,2,3,
%T A321929 1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,1,4,0,0,0,1,0,2,5,0,0,1,2,1,3,5,0,
%U A321929 0,0,1,1,3,6,0,1,1,2,2,3,4,1,1,1,1,1,1
%N A321929 Tetrangle where T(n,H(u),H(v)) is the coefficient of f(v) in s(u), where u and v are integer partitions of n, H is Heinz number, f is forgotten symmetric functions, and s is Schur functions.
%C A321929 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A321929 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e A321929 Tetrangle begins (zeros not shown):
%e A321929   (1): 1
%e A321929 .
%e A321929   (2):    1
%e A321929   (11): 1 1
%e A321929 .
%e A321929   (3):       1
%e A321929   (21):    1 2
%e A321929   (111): 1 1 1
%e A321929 .
%e A321929   (4):            1
%e A321929   (22):     1   1 2
%e A321929   (31):         1 3
%e A321929   (211):    1 1 2 3
%e A321929   (1111): 1 1 1 1 1
%e A321929 .
%e A321929   (5):                 1
%e A321929   (41):              1 4
%e A321929   (32):          1   2 5
%e A321929   (221):       1 2 1 3 5
%e A321929   (311):         1 1 3 6
%e A321929   (2111):    1 1 2 2 3 4
%e A321929   (11111): 1 1 1 1 1 1 1
%e A321929 For example, row 14 gives: s(32) = f(221) + 2f(2111) + 5f(11111).
%Y A321929 This is a regrouping of the triangle A321892.
%Y A321929 Cf. A008480, A056239, A124794, A124795, A153452, A215366, A296188, A300121, A319191, A319193, A321912-A321935.
%K A321929 nonn,tabf
%O A321929 1,11
%A A321929 _Gus Wiseman_, Nov 23 2018