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 A117297 #8 Feb 13 2022 23:15:56 %S A117297 1,1,1,1,2,4,1,3,11,37,1,4,21,122,621,1,5,34,273,2302,16526,1,6,50, %T A117297 508,2763,66482,640207 %N A117297 Triangle read by rows generated from the Narayana transform. %C A117297 The operation used in generating the triangle is analogous to the binomial transform operation used in generating triangle A058127. %F A117297 Let a(1) = 1, then n-th row is generated by performing the operation (M * V) on the (n-1)-th row and extracting the first n terms. M = the Narayana triangle of A001263 considered as a transform. V = the (n-1)-th row of the triangle as a Vector, V; followed by zeros: [a, b, c, 0, 0, 0, ...]. %e A117297 4th row = (1, 3, 11, 37), the first four terms of M * V = (1, 3, 11, 37, 101, 231, 463, ...); where M = the Narayana triangle as an infinitely lower triangular matrix and V = the Vector formed by row 3: [1, 2, 4, 0, 0, 0, ...]. %e A117297 First few rows of the triangle: %e A117297 1; %e A117297 1, 1; %e A117297 1, 2, 4; %e A117297 1, 3, 11, 37; %e A117297 1, 4, 21, 122, 621; %e A117297 1, 5, 34, 273, 2302, 16526; %e A117297 ... %Y A117297 Cf. A001263, A058127. %K A117297 nonn,tabl %O A117297 1,5 %A A117297 _Gary W. Adamson_, Apr 23 2006