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A321921 Tetrangle where T(n,H(u),H(v)) is the coefficient of s(v) in e(u), where u and v are integer partitions of n, H is Heinz number, s is Schur functions, and e is elementary symmetric functions.

%I A321921 #4 Nov 23 2018 07:58:56
%S A321921 1,0,1,1,1,0,0,1,0,1,1,1,2,1,0,0,0,0,1,0,1,0,1,1,0,0,0,1,1,0,1,1,2,1,
%T A321921 1,2,3,3,1,0,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,1,0,1,1,0,0,1,2,1,2,1,0,
%U A321921 0,0,1,1,2,1,0,1,2,3,3,3,1,1,4,5,5,6,4
%N A321921 Tetrangle where T(n,H(u),H(v)) is the coefficient of s(v) in e(u), where u and v are integer partitions of n, H is Heinz number, s is Schur functions, and e is elementary symmetric functions.
%C A321921 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A321921 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e A321921 Tetrangle begins (zeroes not shown):
%e A321921   (1): 1
%e A321921 .
%e A321921   (2):    1
%e A321921   (11): 1 1
%e A321921 .
%e A321921   (3):       1
%e A321921   (21):    1 1
%e A321921   (111): 1 2 1
%e A321921 .
%e A321921   (4):            1
%e A321921   (22):     1   1 1
%e A321921   (31):         1 1
%e A321921   (211):    1 1 2 1
%e A321921   (1111): 1 2 3 3 1
%e A321921 .
%e A321921   (5):                 1
%e A321921   (41):              1 1
%e A321921   (32):          1   1 1
%e A321921   (221):       1 2 1 2 1
%e A321921   (311):         1 1 2 1
%e A321921   (2111):    1 2 3 3 3 1
%e A321921   (11111): 1 4 5 5 6 4 1
%e A321921 For example, row 14 gives: e(32) = s(221) + s(2111) + s(11111).
%Y A321921 This is a regrouping of the triangle A321756.
%Y A321921 Cf. A005651, A008480, A056239, A124794, A124795, A153452, A215366, A296188, A300121, A319191, A319193, A321912-A321935.
%K A321921 nonn,tabf
%O A321921 1,13
%A A321921 _Gus Wiseman_, Nov 22 2018