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

0,2

Comments

See Kreweras (1979) for precise definition.

Links

Table of n, a(n) for n=0..54.

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)

Formula

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

Example

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,
  ...

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 *)

Crossrefs

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

The second row and column are A214824.

Sequence in context: A089848 A033550 A032130 * A184313 A158059 A173323

Adjacent sequences: A259098 A259099 A259100 * A259102 A259103 A259104

Keyword

nonn,tabl,easy

Author

N. J. A. Sloane, Jun 22 2015

Extensions

More terms from Jean-François Alcover, Aug 11 2017

Status

approved