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.

A321752 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of e(v) in p(u), where H is Heinz number, e is elementary symmetric functions, and p is power sum symmetric functions.

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%I A321752 #4 Nov 20 2018 16:30:45
%S A321752 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,-3,1,5,
%T A321752 -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,-4,
%U A321752 1,0,0,-6,6,3,-5,1,0,0,0,0,1,7,-7,-7,-7,14,7,7
%N A321752 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of e(v) in p(u), where H is Heinz number, e is elementary symmetric functions, and p is power sum symmetric functions.
%C A321752 Row n has length A000041(A056239(n)).
%C A321752 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A321752 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e A321752 Triangle begins:
%e A321752    1
%e A321752    1
%e A321752   -2   1
%e A321752    0   1
%e A321752    3  -3   1
%e A321752    0  -2   1
%e A321752   -4   2   4  -4   1
%e A321752    0   0   1
%e A321752    0   4   0  -4   1
%e A321752    0   0   3  -3   1
%e A321752    5  -5  -5   5   5  -5   1
%e A321752    0   0   0  -2   1
%e A321752   -6   6   6   3  -2  -6 -12   9   6  -6   1
%e A321752    0  -4   0   2   4  -4   1
%e A321752    0   0  -6   6   3  -5   1
%e A321752    0   0   0   0   1
%e A321752    7  -7  -7  -7  14   7   7   7  -7  -7 -21  14   7  -7   1
%e A321752    0   0   0   4   0  -4   1
%e A321752 For example, row 15 gives: p(32) = -6e(32) + 6e(221) + 3e(311) - 5e(2111) + e(11111).
%Y A321752 Row sums are A321753.
%Y A321752 Cf. A005651, A008480, A056239, A124794, A124795, A135278, A296150, A319193, A319225, A319226, A321742-A321765, A321854.
%K A321752 sign,tabf
%O A321752 1,3
%A A321752 _Gus Wiseman_, Nov 20 2018