A232223 Triangle read by rows: T(n,k) = number of connected matchings with n crossings and k chords, in a disk.

1, 0, 3, 0, 1, 12, 0, 0, 10, 55, 0, 0, 4, 77, 273, 0, 0, 1, 60, 546, 1428, 0, 0, 0, 35, 624, 3740, 7752, 0, 0, 0, 15, 546, 5600, 25194, 43263, 0, 0, 0, 5, 391, 6405, 46512, 168245, 246675, 0, 0, 0, 1, 240, 6125, 65076, 368676, 1118260, 1430715, 0, 0, 0, 0, 126, 5138, 76296, 606879, 2833600, 7413705, 8414640, 0, 0, 0, 0, 56, 3857, 78880, 834195, 5348420, 21312720, 49085400, 50067108

Offset

1,3

Links

Table of n, a(n) for n=1..78.

V. Pilaud, J. Rué, Analytic combinatorics of chord and hyperchord diagrams with k crossings, arXiv preprint arXiv:1307.6440, 2013

Example

Triangle begins:
1,
0,3,
0,1,12,
0,0,10,55,
0,0,4,77,273,
0,0,1,60,546,1428,
0,0,0,35,624,3740,7752,
0,0,0,15,546,5600,25194,43263,
0,0,0,5,391,6405,46512,168245,246675,
...

Crossrefs

Cf. A232222 (row sums), A000699 (column sums), A322456 (transpose).

Sequence in context: A239731 A327027 A145881 * A245111 A135313 A322670

Adjacent sequences: A232220 A232221 A232222 * A232224 A232225 A232226

Keyword

nonn,tabl

Author

N. J. A. Sloane, Nov 22 2013

Extensions

3 more rows. - R. J. Mathar, Dec 09 2018

Status

approved