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A321924 Tetrangle where T(n,H(u),H(v)) is the coefficient of m(v) in s(u), where u and v are integer partitions of n, H is Heinz number, m is monomial symmetric functions, and s is Schur functions.

%I A321924 #4 Nov 23 2018 07:59:18
%S A321924 1,1,1,0,1,1,1,1,0,1,2,0,0,1,1,1,1,1,1,0,1,0,1,2,0,1,1,2,3,0,0,0,1,3,
%T A321924 0,0,0,0,1,1,1,1,1,1,1,1,0,1,1,2,2,3,4,0,0,1,2,1,3,5,0,0,0,1,0,2,5,0,
%U A321924 0,0,1,1,3,6,0,0,0,0,0,1,4,0,0,0,0,0,0
%N A321924 Tetrangle where T(n,H(u),H(v)) is the coefficient of m(v) in s(u), where u and v are integer partitions of n, H is Heinz number, m is monomial symmetric functions, and s is Schur functions.
%C A321924 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A321924 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e A321924 Tetrangle begins (zeroes not shown):
%e A321924   (1): 1
%e A321924 .
%e A321924   (2):  1 1
%e A321924   (11):   1
%e A321924 .
%e A321924   (3):   1 1 1
%e A321924   (21):    1 2
%e A321924   (111):     1
%e A321924 .
%e A321924   (4):    1 1 1 1 1
%e A321924   (22):     1   1 2
%e A321924   (31):     1 1 2 3
%e A321924   (211):        1 3
%e A321924   (1111):         1
%e A321924 .
%e A321924   (5):     1 1 1 1 1 1 1
%e A321924   (41):      1 1 2 2 3 4
%e A321924   (32):        1 2 1 3 5
%e A321924   (221):         1   2 5
%e A321924   (311):         1 1 3 6
%e A321924   (2111):            1 4
%e A321924   (11111):             1
%e A321924 For example, row 14 gives: s(32) = m(32) + 2m(221) + m(311) + 3m(2111) + 5m(11111).
%Y A321924 This is a regrouping of the triangle A321761.
%Y A321924 Cf. A005651, A008480, A056239, A124794, A124795, A153452, A215366, A296188, A300121, A319191, A319193, A321912-A321935.
%K A321924 nonn,tabf
%O A321924 1,11
%A A321924 _Gus Wiseman_, Nov 22 2018