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 A172380 #13 Nov 11 2022 08:06:51 %S A172380 1,0,1,0,1,1,0,2,3,1,0,5,10,6,1,0,14,36,31,10,1,0,42,137,156,75,15,1, %T A172380 0,132,544,787,510,155,21,1,0,429,2235,4017,3331,1380,287,28,1,0,1430, %U A172380 9445,20809,21405,11411,3255,490,36,1,0,4862,40876,109486,136921,90665 %N A172380 Eigentriangle of Catalan triangle A033184. %C A172380 Row sums are A091768. %C A172380 Production matrix of inverse is matrix with general term (-1)^(n-k+1)C(k,n-k+1). %C A172380 Diagonal sums are A172382. Product of A033184 and A172380 is the matrix A172381. %H A172380 Paul Barry, <a href="http://arxiv.org/abs/1107.5490">Invariant number triangles, eigentriangles and Somos-4 sequences</a>, arXiv preprint arXiv:1107.5490 [math.CO], 2011. %e A172380 Triangle begins %e A172380 1; %e A172380 0, 1; %e A172380 0, 1, 1; %e A172380 0, 2, 3, 1; %e A172380 0, 5, 10, 6, 1; %e A172380 0, 14, 36, 31, 10, 1; %e A172380 0, 42, 137, 156, 75, 15, 1; %e A172380 0, 132, 544, 787, 510, 155, 21, 1; %e A172380 0, 429, 2235, 4017, 3331, 1380, 287, 28, 1; %e A172380 0, 1430, 9445, 20809, 21405, 11411, 3255, 490, 36, 1; %e A172380 Production matrix of inverse is %e A172380 0, 1; %e A172380 0, -1, 1; %e A172380 0, 0, -2, 1; %e A172380 0, 0, 1, -3, 1; %e A172380 0, 0, 0, 3, -4, 1; %e A172380 0, 0, 0, -1, 6, -5, 1; %e A172380 0, 0, 0, 0, -4, 10, -6, 1; %e A172380 0, 0, 0, 0, 1, -10, 15, -7, 1; %e A172380 0, 0, 0, 0, 0, 5, -20, 21, -8, 1; %e A172380 0, 0, 0, 0, 0, -1, 15, -35, 28, -9, 1; %e A172380 0, 0, 0, 0, 0, 0, -6, 35, -56, 36, -10, 1; %K A172380 nonn,tabl %O A172380 0,8 %A A172380 _Paul Barry_, Feb 01 2010