

A213946


A Catalan triangle read by rows, derived from the INVERT transform of initial segments of the Catalan numbers A000108.


0



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, 132, 1, 33, 112, 185, 196, 210, 264, 429, 1, 54, 238, 445, 588, 588, 660, 858, 1430, 1, 88, 496, 1080, 1652, 1764, 1848, 2145, 2860, 4862, 1, 143, 1026, 2610, 4242, 5544, 5544, 6006, 7150, 9724, 16796
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OFFSET

1,5


COMMENTS

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:
1,...1,...1,...1,...1,...1,...
1,...2,...3,...5,...8,..13,...
1,...2,...5,...9,..18,..37,...
1,...2,...5,..14,..28,..62,...
...
Then the rows of the triangle are first differences of the COLUMNS of this array.
Row sums = the Catalan sequence A000108 starting with offset 1. Right border = the Catalan sequence.


LINKS

Table of n, a(n) for n=1..66.


EXAMPLE

First few rows of the triangle are:
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, 132;
1, 33, 112, 185, 196, 210, 264, 429;
1, 54, 238, 445, 588, 588, 660, 858, 1430;
...


CROSSREFS

Cf. A000108.
Sequence in context: A305191 A261357 A238870 * A145036 A272888 A001404
Adjacent sequences: A213943 A213944 A213945 * A213947 A213948 A213949


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Jun 25 2012


EXTENSIONS

Edited by N. J. A. Sloane, Jul 03 2012


STATUS

approved



