A162470 Table read by rows: the Catalan number C(n) followed by pairs (C(n-1-j), C(j+1)), j=0 to n-2.

1, 2, 1, 1, 5, 2, 1, 1, 2, 5, 14, 5, 1, 2, 2, 1, 5, 42, 14, 1, 5, 2, 2, 5, 1, 14, 132, 42, 1, 14, 2, 5, 5, 2, 14, 1, 42, 429, 132, 1, 42, 2, 14, 5, 5, 14, 2, 42, 1, 132, 1430, 429, 1, 132, 2, 42, 5, 14, 14, 5, 42, 2, 132, 1, 429, 4862, 1430, 1, 429, 2, 132, 5, 42, 14, 14, 42, 5, 132, 2

Offset

1,2

Comments

The table starts row n with A000108(n) = C(n) and then visualizes the convolution formula C(n) = sum_{j=0..n-1} C(j)*C(n-1-j) by listing some pairs of that structure in the same row.

Links

Table of n, a(n) for n=1..79.

Example

Starting in row n=1 the table reads
1;
2,1,1;
5,2,1,1,2;
14,5,1,2,2,1,5;
42,14,1,5,2,2,5,1,14;
132,42,1,14,2,5,5,2,14,1,42;
The row n=3 represents 5=2*1+1*1+1*2, for example, where the middle term is not represented in the table.

Crossrefs

cf. A000108.

Sequence in context: A022661 A120292 A179318 * A343234 A174004 A128604

Adjacent sequences: A162467 A162468 A162469 * A162471 A162472 A162473

Keyword

nonn,tabf,less

Author

Juri-Stepan Gerasimov, Jul 04 2009

Extensions

Definition and comment rephrased by R. J. Mathar, Sep 16 2009

Status

approved