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.

A321886 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of m(v) in f(u), where H is Heinz number, m is monomial symmetric functions, and f is forgotten symmetric functions.

This page as a plain text file.
%I A321886 #5 Nov 20 2018 19:46:26
%S A321886 1,1,-1,0,1,1,1,0,0,-2,-1,0,-1,0,0,0,0,1,1,1,1,1,0,0,0,2,0,1,0,0,1,0,
%T A321886 0,0,0,0,0,-3,-2,-2,-1,0,-1,0,0,0,0,0,0,0,0,0,0,-2,-1,0,0,0,0,0,-2,0,
%U A321886 -1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0
%N A321886 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of m(v) in f(u), where H is Heinz number, m is monomial symmetric functions, and f is forgotten symmetric functions.
%C A321886 Row n has length A000041(A056239(n)).
%C A321886 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%C A321886 a(n) is also the coefficient of f(v) in m(u).
%H A321886 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e A321886 Triangle begins:
%e A321886    1
%e A321886    1
%e A321886   -1   0
%e A321886    1   1
%e A321886    1   0   0
%e A321886   -2  -1   0
%e A321886   -1   0   0   0   0
%e A321886    1   1   1
%e A321886    1   1   0   0   0
%e A321886    2   0   1   0   0
%e A321886    1   0   0   0   0   0   0
%e A321886   -3  -2  -2  -1   0
%e A321886   -1   0   0   0   0   0   0   0   0   0   0
%e A321886   -2  -1   0   0   0   0   0
%e A321886   -2   0  -1   0   0   0   0
%e A321886    1   1   1   1   1
%e A321886    1   0   0   0   0   0   0   0   0   0   0   0   0   0   0
%e A321886    3   1   2   1   0   0   0
%e A321886 For example, row 12 gives: f(211) = -3m(4) - 2m(22) - 2m(31) - m(211).
%Y A321886 Row sums are A321887.
%Y A321886 Cf. A005651, A008277, A008480, A048994, A056239, A124794, A124795, A135278, A300121, A319193, A321742-A321765.
%K A321886 sign,tabf
%O A321886 1,10
%A A321886 _Gus Wiseman_, Nov 20 2018