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.

A321746 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of e(v) in m(u), where H is Heinz number, m is monomial symmetric functions, and e is elementary symmetric functions.

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%I A321746 #5 Nov 20 2018 12:21:47
%S A321746 1,1,-2,1,1,0,3,-3,1,-3,1,0,-4,2,4,-4,1,1,0,0,2,1,-2,0,0,4,-2,-1,1,0,
%T A321746 5,-5,-5,5,5,-5,1,-4,0,1,0,0,-6,6,6,3,-2,-6,-12,9,6,-6,1,-5,1,5,-3,-1,
%U A321746 1,0,-5,5,-1,1,-2,0,0,1,0,0,0,0,7,-7,-7,-7,14,7
%N A321746 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of e(v) in m(u), where H is Heinz number, m is monomial symmetric functions, and e is elementary symmetric functions.
%C A321746 Row n has length A000041(A056239(n)).
%C A321746 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%C A321746 Also the coefficient of h(v) in f(u), where h is homogeneous symmetric functions and f is forgotten symmetric functions.
%H A321746 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e A321746 Triangle begins:
%e A321746    1
%e A321746    1
%e A321746   -2   1
%e A321746    1   0
%e A321746    3  -3   1
%e A321746   -3   1   0
%e A321746   -4   2   4  -4   1
%e A321746    1   0   0
%e A321746    2   1  -2   0   0
%e A321746    4  -2  -1   1   0
%e A321746    5  -5  -5   5   5  -5   1
%e A321746   -4   0   1   0   0
%e A321746   -6   6   6   3  -2  -6 -12   9   6  -6   1
%e A321746   -5   1   5  -3  -1   1   0
%e A321746   -5   5  -1   1  -2   0   0
%e A321746    1   0   0   0   0
%e A321746    7  -7  -7  -7  14   7   7   7  -7  -7 -21  14   7  -7   1
%e A321746    5  -3   1   0   0   0   0
%e A321746 For example, row 10 gives: m(31) = 4e(4) - 2e(22) - e(31) + e(211).
%Y A321746 Row sums are A321747.
%Y A321746 Cf. A005651, A008480, A048994, A056239, A124794, A124795, A321738, A321742-A321765, A321854.
%K A321746 sign,tabf
%O A321746 1,3
%A A321746 _Gus Wiseman_, Nov 19 2018