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 A112338 #13 May 04 2024 09:24:05 %S A112338 1,1,1,1,2,1,1,3,5,1,1,4,12,14,1,1,5,22,57,42,1,1,6,35,148,303,132,1, %T A112338 1,7,51,305,1144,1743,429,1,8,70,546,3105,9784,10629,1430,1 %N A112338 Triangle read by rows, generated from A001263. %C A112338 Rows of the array are row sums of n-th powers of the Narayana triangle; e.g., row 1 = A000108: (1, 2, 5, 14, 42, ...); row 2 = row sums of the Narayana triangle squared (A103370): (1, 3, 12, 57, 303, ...), etc. %F A112338 Let M be the infinite lower triangular Narayana triangle (A001263). Perform M^n * [1 0 0 0 ...] getting an array. Take antidiagonals of the array which become rows of the triangle A112338. %e A112338 In the array, antidiagonal terms (1, 3, 5, 1) become row 3 of the triangle. %e A112338 First few rows of the array: %e A112338 1, 1, 1, 1, 1, 1, ... %e A112338 1, 2, 5, 14, 42, 132, ... %e A112338 1, 3, 12, 57, 303, 1743, ... %e A112338 1, 4, 22, 148, 1144, 9784, ... %e A112338 1, 5, 35, 305, 3105, 35505, ... %e A112338 First few rows of the triangle: %e A112338 1; %e A112338 1, 1; %e A112338 1, 2, 1; %e A112338 1, 3, 5, 1; %e A112338 1, 4, 12, 14, 1; %e A112338 1, 5, 22, 57, 42, 1; %e A112338 1, 6, 35, 148, 303, 132, 1; %Y A112338 Cf. A001263, A000326, A005915, A095266, A000108, A103370. %K A112338 nonn,tabl %O A112338 0,5 %A A112338 _Gary W. Adamson_, Sep 04 2005