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%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
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