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.

A321754 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of h(v) in p(u), where H is Heinz number, p is power sum symmetric functions, and h is homogeneous symmetric functions.

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%I A321754 #5 Nov 20 2018 16:31:03
%S A321754 1,1,2,-1,0,1,3,-3,1,0,2,-1,4,-2,-4,4,-1,0,0,1,0,4,0,-4,1,0,0,3,-3,1,
%T A321754 5,-5,-5,5,5,-5,1,0,0,0,2,-1,6,-6,-6,-3,2,6,12,-9,-6,6,-1,0,4,0,-2,-4,
%U A321754 4,-1,0,0,6,-6,-3,5,-1,0,0,0,0,1,7,-7,-7,-7,14
%N A321754 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of h(v) in p(u), where H is Heinz number, p is power sum symmetric functions, and h is homogeneous symmetric functions.
%C A321754 Row n has length A000041(A056239(n)).
%C A321754 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%C A321754 Up to sign, same as A321752.
%H A321754 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e A321754 Triangle begins:
%e A321754    1
%e A321754    1
%e A321754    2  -1
%e A321754    0   1
%e A321754    3  -3   1
%e A321754    0   2  -1
%e A321754    4  -2  -4   4  -1
%e A321754    0   0   1
%e A321754    0   4   0  -4   1
%e A321754    0   0   3  -3   1
%e A321754    5  -5  -5   5   5  -5   1
%e A321754    0   0   0   2  -1
%e A321754    6  -6  -6  -3   2   6  12  -9  -6   6  -1
%e A321754    0   4   0  -2  -4   4  -1
%e A321754    0   0   6  -6  -3   5  -1
%e A321754    0   0   0   0   1
%e A321754    7  -7  -7  -7  14   7   7   7  -7  -7 -21  14   7  -7   1
%e A321754    0   0   0   4   0  -4   1
%e A321754 For example, row 15 gives: p(32) = 6h(32) - 6h(221) - 3h(311) + 5h(2111) - h(11111).
%Y A321754 Row sums are all equal to 1.
%Y A321754 Cf. A005651, A008480, A056239, A124794, A124795, A135278, A319193, A319225, A319226, A321742-A321765, A321854.
%K A321754 sign,tabf
%O A321754 1,3
%A A321754 _Gus Wiseman_, Nov 20 2018