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 A134634 #12 Feb 11 2024 06:59:18 %S A134634 1,1,1,2,2,2,5,4,4,5,14,9,8,9,14,42,23,17,17,23,42,132,65,40,34,40,65, %T A134634 132,429,197,105,74,74,105,197,429,1430,626,302,179,148,179,302,626, %U A134634 1430,4862,2056,928,481,327,327,481,928,2056,4862,16796,6918,2984,1409,808,654,808,1409,2984,6918,16796,58786,23714,9902,4393,2217,1462,1462,2217,4393,9902,23714,58786 %N A134634 Triangle formed by Pascal's rule with borders = A000108. %C A134634 Row sums = A134635: (1, 2, 6, 18, 54, 164, ...). %F A134634 Triangle, given right and left borders consist of the Catalan sequence, A000108; then T(n,k) = T(n-1,k) + T(n-1,k-1). %e A134634 First few rows of the triangle: %e A134634 1; %e A134634 1, 1; %e A134634 2, 2, 2; %e A134634 5, 4, 4, 5; %e A134634 14, 9, 8, 9, 14; %e A134634 42, 23, 17, 17, 23, 42; %e A134634 132, 65, 40, 34, 40, 65, 132; %e A134634 ... %Y A134634 Cf. A000108, A134635, A222403, A222404, A222405. %K A134634 nonn,tabl %O A134634 0,4 %A A134634 _Gary W. Adamson_, Nov 04 2007 %E A134634 Recomputed by _N. J. A. Sloane_, Feb 18 2013