%I
%S 1,1,1,1,2,2,1,4,4,5,1,7,10,10,14,1,12,24,25,28,42,1,20,52,70,70,84,
%T 132,1,33,112,185,196,210,264,429,1,54,238,445,588,588,660,858,1430,1,
%U 88,496,1080,1652,1764,1848,2145,2860,4862,1,143,1026,2610,4242,5544,5544,6006,7150,9724,16796
%N A Catalan triangle read by rows, derived from the INVERT transform of initial segments of the Catalan numbers A000108.
%C Create an array in which the nth row (n >= 1) is the INVERT transform of the first n terms of A000108: (1, 1, 2, 5, 14,...) followed by zeros. For example, row 3 of the array is the INVERT transform of (1, 1, 2, 0, 0, 0,...). The array is:
%C 1,...1,...1,...1,...1,...1,...
%C 1,...2,...3,...5,...8,..13,...
%C 1,...2,...5,...9,..18,..37,...
%C 1,...2,...5,..14,..28,..62,...
%C ...
%C Then the rows of the triangle are first differences of the COLUMNS of this array.
%C Row sums = the Catalan sequence A000108 starting with offset 1. Right border = the Catalan sequence.
%e First few rows of the triangle are:
%e 1;
%e 1, 1;
%e 1, 2, 2;
%e 1, 4, 4, 5;
%e 1, 7, 10, 10, 14;
%e 1, 12, 24, 25, 28, 42;
%e 1, 20, 52, 70, 70, 84, 132;
%e 1, 33, 112, 185, 196, 210, 264, 429;
%e 1, 54, 238, 445, 588, 588, 660, 858, 1430;
%e ...
%Y Cf. A000108.
%K nonn,tabl
%O 1,5
%A _Gary W. Adamson_, Jun 25 2012
%E Edited by _N. J. A. Sloane_, Jul 03 2012
