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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 (list; table; graph; refs; listen; history; text; internal format)
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 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

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Last modified December 7 00:43 EST 2019. Contains 329816 sequences. (Running on oeis4.)