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.

A321896 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of p(v) in e(u) * Product_i u_i!, where H is Heinz number, e is elementary symmetric functions, and p is power sum symmetric functions.

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%I A321896 #5 Nov 21 2018 09:24:44
%S A321896 1,1,-1,1,0,1,2,-3,1,0,-1,1,-6,3,8,-6,1,0,0,1,0,1,0,-2,1,0,0,2,-3,1,
%T A321896 24,-30,-20,15,20,-10,1,0,0,0,-1,1,-120,90,144,40,-15,-90,-120,45,40,
%U A321896 -15,1,0,-6,0,3,8,-6,1,0,0,-2,3,2,-4,1,0,0,0,0,1,720
%N A321896 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of p(v) in e(u) * Product_i u_i!, where H is Heinz number, e is elementary symmetric functions, and p is power sum symmetric functions.
%C A321896 Row n has length A000041(A056239(n)).
%C A321896 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A321896 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e A321896 Triangle begins:
%e A321896      1
%e A321896      1
%e A321896     -1    1
%e A321896      0    1
%e A321896      2   -3    1
%e A321896      0   -1    1
%e A321896     -6    3    8   -6    1
%e A321896      0    0    1
%e A321896      0    1    0   -2    1
%e A321896      0    0    2   -3    1
%e A321896     24  -30  -20   15   20  -10    1
%e A321896      0    0    0   -1    1
%e A321896   -120   90  144   40  -15  -90 -120   45   40  -15    1
%e A321896      0   -6    0    3    8   -6    1
%e A321896      0    0   -2    3    2   -4    1
%e A321896      0    0    0    0    1
%e A321896    720 -840 -504 -420  630  504  210  280 -105 -210 -420  105   70  -21    1
%e A321896      0    0    0    1    0   -2    1
%e A321896 For example, row 15 gives: 12e(32) = -2p(32) + 3p(221) + 2p(311) - 4p(2111) + p(11111).
%Y A321896 Row sums are A036987.
%Y A321896 Cf. A005651, A008480, A056239, A124794, A124795, A135278, A319193, A319225, A319226, A321742-A321765, A321897.
%K A321896 sign,tabf
%O A321896 1,7
%A A321896 _Gus Wiseman_, Nov 20 2018