A259101 Square array read by antidiagonals arising in the enumeration of corners.

1, 2, 2, 5, 16, 5, 14, 91, 91, 14, 42, 456, 936, 456, 42, 132, 2145, 7425, 7425, 2145, 132, 429, 9724, 50765, 85800, 50765, 9724, 429, 1430, 43043, 315315, 805805, 805805, 315315, 43043, 1430, 4862, 187408, 1831648, 6584032, 9962680, 6584032, 1831648, 187408, 4862, 16796, 806208, 10127988, 48674808, 103698504, 103698504, 48674808, 10127988, 806208, 16796

Offset: 0

Author

N. J. A. Sloane, Jun 22 2015

Keywords

• nonn
• tabl
• easy

Comments

See Kreweras (1979) for precise definition.

Examples

			The first few antidiagonals are:
    1,
    2,    2,
    5,   16,    5,
   14,   91,   91,   14,
   42,  456,  936,  456,   42,
  132, 2145, 7425, 7425, 2145, 132,
  ...
		

Links

• G. Kreweras, Sur les extensions linéaires d'une famille particulière d'ordres partiels, Discrete Math., 27 (1979), 279-295.
• G. Kreweras, Sur les extensions linéaires d'une famille particulière d'ordres partiels, Discrete Math., 27 (1979), 279-295. (Annotated scanned copy)

Crossrefs

The first row and column of the array are the Catalan numbers A000108.

The second row and column are A214824.

Programs

Mathematica

a[x_, y_] := (2(2x+2y+1)!(x^2+3x*y+y^2+4x+4y+3)) / (x!(x+1)!y!(y+1)!(x+y+1)(x+y+2)(x+y+3));
Table[Table[a[x-y, y], {y, 0, x}] // Reverse, {x, 0, 9}] // Flatten (* Jean-François Alcover, Aug 11 2017 *)

Formula

Kreweras gives an explicit formula for the general term (see bottom display on page 291).

Extensions

More terms from Jean-François Alcover, Aug 11 2017