cp's OEIS Frontend

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

%I A259101 #21 Nov 07 2017 02:59:46
%S A259101 1,2,2,5,16,5,14,91,91,14,42,456,936,456,42,132,2145,7425,7425,2145,
%T A259101 132,429,9724,50765,85800,50765,9724,429,1430,43043,315315,805805,
%U A259101 805805,315315,43043,1430,4862,187408,1831648,6584032,9962680,6584032,1831648,187408,4862,16796,806208,10127988,48674808,103698504,103698504,48674808,10127988,806208,16796
%N A259101 Square array read by antidiagonals arising in the enumeration of corners.
%C A259101 See Kreweras (1979) for precise definition.
%H A259101 G. Kreweras, <a href="http://dx.doi.org/10.1016/0012-365X(79)90163-8">Sur les extensions linéaires d'une famille particulière d'ordres partiels</a>, Discrete Math., 27 (1979), 279-295.
%H A259101 G. Kreweras, <a href="/A006330/a006330_1.pdf">Sur les extensions linéaires d'une famille particulière d'ordres partiels</a>, Discrete Math., 27 (1979), 279-295. (Annotated scanned copy)
%F A259101 Kreweras gives an explicit formula for the general term (see bottom display on page 291).
%e A259101 The first few antidiagonals are:
%e A259101     1,
%e A259101     2,    2,
%e A259101     5,   16,    5,
%e A259101    14,   91,   91,   14,
%e A259101    42,  456,  936,  456,   42,
%e A259101   132, 2145, 7425, 7425, 2145, 132,
%e A259101   ...
%t A259101 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));
%t A259101 Table[Table[a[x-y, y], {y, 0, x}] // Reverse, {x, 0, 9}] // Flatten (* _Jean-François Alcover_, Aug 11 2017 *)
%Y A259101 The first row and column of the array are the Catalan numbers A000108.
%Y A259101 The second row and column are A214824.
%K A259101 nonn,tabl,easy
%O A259101 0,2
%A A259101 _N. J. A. Sloane_, Jun 22 2015
%E A259101 More terms from _Jean-François Alcover_, Aug 11 2017