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%I #21 May 04 2024 09:23:51
%S 1,1,1,1,2,1,1,4,2,1,1,7,5,2,1,1,11,13,5,2,1,1,16,31,14,5,2,1,1,22,66,
%T 41,14,5,2,1,1,29,127,116,42,14,5,2,1,1,37,225,302,131,42,14,5,2,1,1,
%U 46,373,715,407,132,42,14,5,2,1,1,56,586,1549,1205,428,132,42,14,5,2,1
%N Triangle read by rows, generated from the Narayana triangle as a matrix.
%C The n-th column starting from the top has the first n terms in the Catalan sequence: (1, 2, 5, 14, ...)
%F n-th column (offset) is generated by P * V; P = the Narayana triangle as an infinite lower triangular matrix, V = vector for n-th column comprising n leading 1's and the rest zeros (e.g., V for 3rd column = [1, 1, 1, 0, 0, 0, ...].
%e Col. 2 offset = 1, 2, 4, 7, 11, 16, 22, ... since P * [1, 1, 0, 0, 0, ...] = 1, 2, 4, 7, 11, ...
%e First few rows of the triangle are:
%e 1;
%e 1, 1;
%e 1, 2, 1;
%e 1, 4, 2, 1;
%e 1, 7, 5, 2, 1;
%e 1, 11, 13, 5, 2, 1;
%e 1, 16, 31, 14, 5, 2, 1;
%e ...
%e Second column = A000124.
%Y Cf. A000108, A000124, A001263, A137940.
%K nonn,tabl
%O 1,5
%A _Gary W. Adamson_, May 01 2005
%E More terms from _Alois P. Heinz_, Nov 28 2021
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