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.

A321894 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of s(v) in f(u), where H is Heinz number, f is forgotten symmetric functions, and s is Schur functions.

This page as a plain text file.
%I A321894 #5 Nov 21 2018 09:24:31
%S A321894 1,1,-1,1,1,0,1,-1,1,-2,1,0,-1,0,1,-1,1,1,0,0,1,1,-1,0,0,2,-1,-1,1,0,
%T A321894 1,-1,0,0,1,-1,1,-3,0,1,0,0,-1,0,1,0,0,-1,0,0,1,-1,1,-2,1,1,-1,-1,1,0,
%U A321894 -2,2,-1,1,-1,0,0
%N A321894 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of s(v) in f(u), where H is Heinz number, f is forgotten symmetric functions, and s is Schur functions.
%C A321894 Row n has length A000041(A056239(n)).
%C A321894 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A321894 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e A321894 Triangle begins:
%e A321894    1
%e A321894    1
%e A321894   -1   1
%e A321894    1   0
%e A321894    1  -1   1
%e A321894   -2   1   0
%e A321894   -1   0   1  -1   1
%e A321894    1   0   0
%e A321894    1   1  -1   0   0
%e A321894    2  -1  -1   1   0
%e A321894    1  -1   0   0   1  -1   1
%e A321894   -3   0   1   0   0
%e A321894   -1   0   1   0   0  -1   0   0   1  -1   1
%e A321894   -2   1   1  -1  -1   1   0
%e A321894   -2   2  -1   1  -1   0   0
%e A321894 For example, row 15 gives: f(32) = -2s(5) - s(32) + 2s(41) + s(221) - s(311).
%Y A321894 Row sums are A321764.
%Y A321894 Cf. A000085, A008480, A056239, A082733, A124795, A153452, A296188, A300121, A317552, A321742-A321765, A321892.
%K A321894 sign,tabf,more
%O A321894 1,10
%A A321894 _Gus Wiseman_, Nov 20 2018