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.

A321918 Tetrangle where T(n,H(u),H(v)) is the coefficient of e(v) in p(u), where u and v are integer partitions of n, H is Heinz number, e is elementary symmetric functions, and p is power sum symmetric functions.

This page as a plain text file.
%I A321918 #4 Nov 22 2018 18:18:13
%S A321918 1,-2,1,0,1,3,-3,1,0,-2,1,0,0,1,-4,2,4,-4,1,0,4,0,-4,1,0,0,3,-3,1,0,0,
%T A321918 0,-2,1,0,0,0,0,1,5,-5,-5,5,5,-5,1,0,-4,0,2,4,-4,1,0,0,-6,6,3,-5,1,0,
%U A321918 0,0,4,0,-4,1,0,0,0,0,3,-3,1,0,0,0,0,0,-2,1
%N A321918 Tetrangle where T(n,H(u),H(v)) is the coefficient of e(v) in p(u), where u and v are integer partitions of n, H is Heinz number, e is elementary symmetric functions, and p is power sum symmetric functions.
%C A321918 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A321918 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e A321918 Tetrangle begins (zeroes not shown):
%e A321918   (1):  1
%e A321918 .
%e A321918   (2):  -2  1
%e A321918   (11):     1
%e A321918 .
%e A321918   (3):    3 -3  1
%e A321918   (21):     -2  1
%e A321918   (111):        1
%e A321918 .
%e A321918   (4):    -4  2  4 -4  1
%e A321918   (22):       4    -4  1
%e A321918   (31):          3 -3  1
%e A321918   (211):           -2  1
%e A321918   (1111):              1
%e A321918 .
%e A321918   (5):      5 -5 -5  5  5 -5  1
%e A321918   (41):       -4     2  4 -4  1
%e A321918   (32):          -6  6  3 -5  1
%e A321918   (221):             4    -4  1
%e A321918   (311):                3 -3  1
%e A321918   (2111):                 -2  1
%e A321918   (11111):                    1
%e A321918 For example, row 14 gives: p(32) = -6e(32) + 6e(221) + 3e(311) - 5e(2111) + e(11111).
%Y A321918 This is a regrouping of the triangle A321752.
%Y A321918 Cf. A005651, A008480, A056239, A124794, A124795, A135278, A215366, A318284, A319191, A319193, A319225, A319226, A321912-A321935.
%K A321918 sign,tabf
%O A321918 1,2
%A A321918 _Gus Wiseman_, Nov 22 2018