A259992 - OEIS

%I #26 Dec 28 2017 18:46:09

%S 1,1,2,1,2,6,8,4,1,5,20,36,38,21,6,1,14,70,160,220,202,116,40,8,1,42,

%T 252,700,1190,1380,1152,670,260,65,10,1,132,924,3024,6132,8610,8862,

%U 6904,4012,1680,490,96,12,1,429,3432,12936,30492,50316,61656,58072

%N Irregular triangle read by rows: T(n,k) = number of Havender tableaux of height 2 with n columns and k empty squares (n >= 0, 0 <= k <= 2*n).

%D D. Gouyou-Beauchamps, "Tableaux de Havender standards," in S. Brlek, editor, Parallélisme: Modèles et Complexité. LACIM, Université du Québec à Montréal, 1989.

%H Alois P. Heinz, <a href="/A259992/b259992.txt">Rows n = 0..100, flattened</a>

%H D. Gouyou-Beauchamps, <a href="/A007345/a007345.pdf">Tableaux de Havender standards</a>, Parallélisme: Modèles et Complexité. LACIM, Université du Québec à Montréal, 1989. (Annotated scanned copy)

%F T(n,k) = v(2 * n, 2 * n - k) where v(p, k) = Sum_{j=max(0, k-p)..floor(k/2)} (2*k-2*j)! * p! / ((p - k + j)! * (k-2*j)! * (j+1)! * ((k-j)!)^2). - _Sean A. Irvine_, Dec 28 2017

%e Triangle begins:

%e :   1;

%e :   1,   2,    1;

%e :   2,   6,    8,    4,    1;

%e :   5,  20,   36,   38,   21,    6,    1;

%e :  14,  70,  160,  220,  202,  116,   40,    8,    1;

%e :  42, 252,  700, 1190, 1380, 1152,  670,  260,   65,  10,  1;

%e : 132, 924, 3024, 6132, 8610, 8862, 6904, 4012, 1680, 490, 96, 12, 1;

%e : ...

%Y Row sums are A007345.

%Y Column k=0 gives A000108.

%K nonn,tabf

%O 0,3

%A _N. J. A. Sloane_, Jul 13 2015