A232222 -id:A232222

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A232223

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

+10
3

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

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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:

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).

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Nov 22 2013

EXTENSIONS

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

STATUS

approved

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