A213946 A Catalan triangle read by rows, derived from the INVERT transform of initial segments of the Catalan numbers A000108.

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

Offset

1,5

Comments

Create an array in which the n-th 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 A341146 A355276

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