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.

A321916 Tetrangle where T(n,H(u),H(v)) is the coefficient of e(v) in h(u), where u and v are integer partitions of n, H is Heinz number, e is elementary symmetric functions, and h is homogeneous symmetric functions.

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%I A321916 #4 Nov 22 2018 18:17:58
%S A321916 1,-1,1,0,1,1,-2,1,0,-1,1,0,0,1,-1,1,2,-3,1,0,1,0,-2,1,0,0,1,-2,1,0,0,
%T A321916 0,-1,1,0,0,0,0,1,1,-2,-2,3,3,-4,1,0,-1,0,1,2,-3,1,0,0,-1,2,1,-3,1,0,
%U A321916 0,0,1,0,-2,1,0,0,0,0,1,-2,1,0,0,0,0,0,-1,1
%N A321916 Tetrangle where T(n,H(u),H(v)) is the coefficient of e(v) in h(u), where u and v are integer partitions of n, H is Heinz number, e is elementary symmetric functions, and h is homogeneous symmetric functions.
%C A321916 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%C A321916 Also the coefficient of h(v) in e(u).
%H A321916 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e A321916 Tetrangle begins (zeroes not shown):
%e A321916   (1):  1
%e A321916 .
%e A321916   (2):  -1  1
%e A321916   (11):     1
%e A321916 .
%e A321916   (3):    1 -2  1
%e A321916   (21):     -1  1
%e A321916   (111):        1
%e A321916 .
%e A321916   (4):    -1  1  2 -3  1
%e A321916   (22):       1    -2  1
%e A321916   (31):          1 -2  1
%e A321916   (211):           -1  1
%e A321916   (1111):              1
%e A321916 .
%e A321916   (5):      1 -2 -2  3  3 -4  1
%e A321916   (41):       -1     1  2 -3  1
%e A321916   (32):          -1  2  1 -3  1
%e A321916   (221):             1    -2  1
%e A321916   (311):                1 -2  1
%e A321916   (2111):                 -1  1
%e A321916   (11111):                    1
%e A321916 For example, row 14 gives: h(32) = -e(32) + 2e(221) + e(311) - 3e(2111) + e(11111).
%Y A321916 This is a regrouping of the triangle A321749. Row sums are A134286.
%Y A321916 Cf. A005651, A008480, A056239, A124794, A124795, A215366, A318284, A318360, A319191, A319193, A321912-A321935.
%K A321916 sign,tabf
%O A321916 1,7
%A A321916 _Gus Wiseman_, Nov 22 2018