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.

A321749 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of e(v) in h(u) or, equivalently, the coefficient of h(v) in e(u), where H is Heinz number, e is elementary symmetric functions, and h is homogeneous symmetric functions.

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%I A321749 #6 Nov 20 2018 16:30:23
%S A321749 1,1,-1,1,0,1,1,-2,1,0,-1,1,-1,1,2,-3,1,0,0,1,0,1,0,-2,1,0,0,1,-2,1,1,
%T A321749 -2,-2,3,3,-4,1,0,0,0,-1,1,-1,2,2,1,-1,-3,-6,6,4,-5,1,0,-1,0,1,2,-3,1,
%U A321749 0,0,-1,2,1,-3,1,0,0,0,0,1,1,-2,-2,-2,6,3,3
%N A321749 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of e(v) in h(u) or, equivalently, the coefficient of h(v) in e(u), where H is Heinz number, e is elementary symmetric functions, and h is homogeneous symmetric functions.
%C A321749 Row n has length A000041(A056239(n)).
%C A321749 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A321749 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e A321749 Triangle begins:
%e A321749    1
%e A321749    1
%e A321749   -1   1
%e A321749    0   1
%e A321749    1  -2   1
%e A321749    0  -1   1
%e A321749   -1   1   2  -3   1
%e A321749    0   0   1
%e A321749    0   1   0  -2   1
%e A321749    0   0   1  -2   1
%e A321749    1  -2  -2   3   3  -4   1
%e A321749    0   0   0  -1   1
%e A321749   -1   2   2   1  -1  -3  -6   6   4  -5   1
%e A321749    0  -1   0   1   2  -3   1
%e A321749    0   0  -1   2   1  -3   1
%e A321749    0   0   0   0   1
%e A321749    1  -2  -2  -2   6   3   3   3  -4  -4 -12  10   5  -6   1
%e A321749    0   0   0   1   0  -2   1
%e A321749 For example, row 14 gives: h(41) = -e(41) + e(221) + 2e(311) - 3e(2111) + e(11111).
%Y A321749 Row sums are A036987.
%Y A321749 Cf. A005651, A008480, A048994, A056239, A124794, A124795, A135278, A319191, A319193, A321742-A321765.
%K A321749 sign,tabf
%O A321749 1,8
%A A321749 _Gus Wiseman_, Nov 20 2018