|
Search: id:A079267
|
|
|
| A079267 |
|
d(n,s) = number of perfect matchings on {1, 2, ..., n} with k short pairs. |
|
+0
3
|
|
| 1, 0, 1, 1, 1, 1, 5, 6, 3, 1, 36, 41, 21, 6, 1, 329, 365, 185, 55, 10, 1, 3655, 3984, 2010, 610, 120, 15, 1, 47844, 51499, 25914, 7980, 1645, 231, 21, 1
(list; table; graph; listen)
|
|
|
OFFSET
|
0,7
|
|
|
COMMENT
|
Read backwards, the n-th row of the triangle gives the Hilbert series of the variety of slopes determined by n points in the plane.
|
|
REFERENCES
|
G. Kreweras and Y. Poupard, Sur les partitions en paires d'un ensemble fini totalement ordonne, Publications de l'Institut de Statistique de l'Universit\'{e} de Paris, 23 (1978), 57-74
J. L. Martin, The slopes determined by n points in the plane, preprint, 2003.
|
|
LINKS
|
J. L. Martin, The slopes determined by n points in the plane.
|
|
FORMULA
|
d(n, s) = 1/s! * sum(((-1)^(h-s)*(2*n-h)!/(2^(n-h)*(n-h)!*(h-s)!)), h=s..n)
E.g.f.: exp((x-1)*(1-sqrt(1-2*y)))/sqrt(1-2*y). [From Vladeta Jovovic (vladeta(AT)eunet.yu), Dec 15 2008]
|
|
EXAMPLE
|
Triangle begins:
1
0 1
1 1 1
5 6 3 1
36 41 21 6 1
|
|
MAPLE
|
d := (n, s) -> 1/s! * sum('((-1)^(h-s)*(2*n-h)!/(2^(n-h)*(n-h)!*(h-s)!))', 'h'=s..n):
|
|
CROSSREFS
|
Row sums are A001147. Columns are A000806, A006198, A006199, A006200.
Sequence in context: A018851 A011499 A106599 this_sequence A060296 A152061 A114598
Adjacent sequences: A079264 A079265 A079266 this_sequence A079268 A079269 A079270
|
|
KEYWORD
|
easy,nice,nonn,tabl
|
|
AUTHOR
|
Jeremy Martin (martin(AT)math.umn.edu), Feb 05 2003
|
|
|
Search completed in 0.002 seconds
|
