cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A321912 Tetrangle where T(n,H(u),H(v)) is the coefficient of m(v) in e(u), where u and v are integer partitions of n, H is Heinz number, m is monomial symmetric functions, and e is elementary symmetric functions.

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%I A321912 #5 Nov 22 2018 18:17:30
%S A321912 1,0,1,1,2,0,0,1,0,1,3,1,3,6,0,0,0,0,1,0,1,0,2,6,0,0,0,1,4,0,2,1,5,12,
%T A321912 1,6,4,12,24,0,0,0,0,0,0,1,0,0,0,0,0,1,5,0,0,0,1,0,3,10,0,0,1,5,2,12,
%U A321912 30,0,0,0,2,1,7,20,0,1,3,12,7,27,60,1,5
%N A321912 Tetrangle where T(n,H(u),H(v)) is the coefficient of m(v) in e(u), where u and v are integer partitions of n, H is Heinz number, m is monomial symmetric functions, and e is elementary symmetric functions.
%C A321912 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%C A321912 Also the coefficient of f(v) in h(u), where f is forgotten symmetric functions and h is homogeneous symmetric functions.
%H A321912 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e A321912 Tetrangle begins (zeroes not shown):
%e A321912   (1):  1
%e A321912 .
%e A321912   (2):      1
%e A321912   (11):  1  2
%e A321912 .
%e A321912   (3):          1
%e A321912   (21):      1  3
%e A321912   (111):  1  3  6
%e A321912 .
%e A321912   (4):                 1
%e A321912   (22):       1     2  6
%e A321912   (31):             1  4
%e A321912   (211):      2  1  5 12
%e A321912   (1111):  1  6  4 12 24
%e A321912 .
%e A321912   (5):                        1
%e A321912   (41):                    1  5
%e A321912   (32):              1     3 10
%e A321912   (221):          1  5  2 12 30
%e A321912   (311):             2  1  7 20
%e A321912   (2111):      1  3 12  7 27 60
%e A321912   (11111):  1  5 10 30 20 60 20
%e A321912 For example, row 14 gives: e(32) = m(221) + 3m(2111) + 10m(11111).
%Y A321912 This is a regrouping of the triangle A321742.
%Y A321912 Cf. A005651, A008480, A056239, A124794, A124795, A215366, A318284, A318360, A319191, A319193, A321854, A321738, A321913-A321935.
%K A321912 nonn,tabf
%O A321912 1,5
%A A321912 _Gus Wiseman_, Nov 22 2018