A134634 Triangle formed by Pascal's rule with borders = A000108.

1, 1, 1, 2, 2, 2, 5, 4, 4, 5, 14, 9, 8, 9, 14, 42, 23, 17, 17, 23, 42, 132, 65, 40, 34, 40, 65, 132, 429, 197, 105, 74, 74, 105, 197, 429, 1430, 626, 302, 179, 148, 179, 302, 626, 1430, 4862, 2056, 928, 481, 327, 327, 481, 928, 2056, 4862, 16796, 6918, 2984, 1409, 808, 654, 808, 1409, 2984, 6918, 16796, 58786, 23714, 9902, 4393, 2217, 1462, 1462, 2217, 4393, 9902, 23714, 58786

Offset

0,4

Comments

Row sums = A134635: (1, 2, 6, 18, 54, 164, ...).

Links

Table of n, a(n) for n=0..77.

Formula

Triangle, given right and left borders consist of the Catalan sequence, A000108; then T(n,k) = T(n-1,k) + T(n-1,k-1).

Example

First few rows of the triangle:
    1;
    1,  1;
    2,  2,  2;
    5,  4,  4,  5;
   14,  9,  8,  9, 14;
   42, 23, 17, 17, 23, 42;
  132, 65, 40, 34, 40, 65, 132;
  ...

Crossrefs

Cf. A000108, A134635, A222403, A222404, A222405.

Sequence in context: A209772 A370164 A147293 * A346500 A103286 A285704

Adjacent sequences: A134631 A134632 A134633 * A134635 A134636 A134637

Keyword

nonn,tabl

Author

Gary W. Adamson, Nov 04 2007

Extensions

Recomputed by N. J. A. Sloane, Feb 18 2013

Status

approved