Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #8 Feb 13 2022 23:15:56
%S 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 508,2763,66482,640207
%N Triangle read by rows generated from the Narayana transform.
%C The operation used in generating the triangle is analogous to the binomial transform operation used in generating triangle A058127.
%F 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 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 First few rows of the triangle:
%e 1;
%e 1, 1;
%e 1, 2, 4;
%e 1, 3, 11, 37;
%e 1, 4, 21, 122, 621;
%e 1, 5, 34, 273, 2302, 16526;
%e ...
%Y Cf. A001263, A058127.
%K nonn,tabl
%O 1,5
%A _Gary W. Adamson_, Apr 23 2006