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.
%I A321900 #4 Nov 21 2018 09:25:14 %S A321900 1,1,1,1,-1,1,2,3,1,-1,0,1,6,3,8,6,1,2,-3,1,0,3,-4,0,1,-2,-1,0,2,1,24, %T A321900 30,20,15,20,10,1,2,-1,0,-2,1,120,90,144,40,15,90,120,45,40,15,1,-6,0, %U A321900 -5,0,5,5,1,0,-6,4,3,-4,2,1,-6,3,8,-6,1,720,840 %N A321900 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of p(v) in S(u), where H is Heinz number, p is power sum symmetric functions, and S is augmented Schur functions. %C A321900 Row n has length A000041(A056239(n)). %C A321900 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k). %C A321900 We define the augmented Schur functions to be S(y) = |y|! * s(y) / syt(y), where s is Schur functions and syt(y) is the number of standard Young tableaux of shape y. %H A321900 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a> %e A321900 Triangle begins: %e A321900 1 %e A321900 1 %e A321900 1 1 %e A321900 -1 1 %e A321900 2 3 1 %e A321900 -1 0 1 %e A321900 6 3 8 6 1 %e A321900 2 -3 1 %e A321900 0 3 -4 0 1 %e A321900 -2 -1 0 2 1 %e A321900 24 30 20 15 20 10 1 %e A321900 2 -1 0 -2 1 %e A321900 120 90 144 40 15 90 120 45 40 15 1 %e A321900 -6 0 -5 0 5 5 1 %e A321900 0 -6 4 3 -4 2 1 %e A321900 -6 3 8 -6 1 %e A321900 720 840 504 420 630 504 210 280 105 210 420 105 70 21 1 %e A321900 0 6 -4 3 -4 -2 1 %e A321900 For example, row 15 gives: S(32) = 4p(32) - 6p(41) + 3p(221) - 4p(311) + 2p(2111) + p(11111). %Y A321900 Row sums are above. %Y A321900 Cf. A000085, A008480, A056239, A082733, A124795, A153452, A296188, A296561, A300121, A304438, A317552, A317554, A321742-A321765. %K A321900 sign,tabf %O A321900 1,7 %A A321900 _Gus Wiseman_, Nov 20 2018