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.

A321932 Tetrangle where T(n,H(u),H(v)) is the coefficient of p(v) in e(u) * Product_i u_i!, where u and v are integer partitions of n, H is Heinz number, p is power sum symmetric functions, and e is elementary symmetric functions.

This page as a plain text file.
%I A321932 #6 Nov 23 2018 21:13:47
%S A321932 1,-1,1,0,1,2,-3,1,0,-1,1,0,0,1,-6,3,8,-6,1,0,1,0,-2,1,0,0,2,-3,1,0,0,
%T A321932 0,-1,1,0,0,0,0,1,24,-30,-20,15,20,-10,1,0,-6,0,3,8,-6,1,0,0,-2,3,2,
%U A321932 -4,1,0,0,0,1,0,-2,1,0,0,0,0,2,-3,1,0,0,0,0,0
%N A321932 Tetrangle where T(n,H(u),H(v)) is the coefficient of p(v) in e(u) * Product_i u_i!, where u and v are integer partitions of n, H is Heinz number, p is power sum symmetric functions, and e is elementary symmetric functions.
%C A321932 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A321932 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e A321932 Tetrangle begins (zeros not shown):
%e A321932   (1):  1
%e A321932 .
%e A321932   (2):  -1  1
%e A321932   (11):     1
%e A321932 .
%e A321932   (3):    2 -3  1
%e A321932   (21):     -1  1
%e A321932   (111):        1
%e A321932 .
%e A321932   (4):    -6  3  8 -6  1
%e A321932   (22):       1    -2  1
%e A321932   (31):          2 -3  1
%e A321932   (211):           -1  1
%e A321932   (1111):              1
%e A321932 .
%e A321932   (5):     24 30 20 15 20 10  1
%e A321932   (41):       -6     3  8 -6  1
%e A321932   (32):          -2  3  2 -4  1
%e A321932   (221):             1    -2  1
%e A321932   (311):                2 -3  1
%e A321932   (2111):                 -1  1
%e A321932   (11111):                    1
%e A321932 For example, row 14 gives: 12e(32) = -2p(32) + 3p(221) + 2p(311) - 4p(2111) + p(11111).
%Y A321932 Row sums are A134286. This is a regrouping of the triangle A321896.
%Y A321932 Cf. A008480, A056239, A124794, A124795, A215366, A318284, A318360, A319191, A319193, A321912-A321935.
%K A321932 sign,tabf
%O A321932 1,6
%A A321932 _Gus Wiseman_, Nov 23 2018