A259992 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).

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, 252, 700, 1190, 1380, 1152, 670, 260, 65, 10, 1, 132, 924, 3024, 6132, 8610, 8862, 6904, 4012, 1680, 490, 96, 12, 1, 429, 3432, 12936, 30492, 50316, 61656, 58072

Offset

0,3

References

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

Links

Alois P. Heinz, Rows n = 0..100, flattened

D. Gouyou-Beauchamps, Tableaux de Havender standards, Parallélisme: Modèles et Complexité. LACIM, Université du Québec à Montréal, 1989. (Annotated scanned copy)

Formula

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

Example

Triangle begins:
:   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, 252,  700, 1190, 1380, 1152,  670,  260,   65,  10,  1;
: 132, 924, 3024, 6132, 8610, 8862, 6904, 4012, 1680, 490, 96, 12, 1;
: ...

Crossrefs

Row sums are A007345.

Column k=0 gives A000108.

Sequence in context: A059587 A070236 A020825 * A110422 A131804 A307519

Adjacent sequences: A259989 A259990 A259991 * A259993 A259994 A259995

Keyword

nonn,tabf

Author

N. J. A. Sloane, Jul 13 2015

Status

approved