Search: id:A079267
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%I A079267
%S A079267 1,0,1,1,1,1,5,6,3,1,36,41,21,6,1,329,365,185,55,10,1,3655,3984,2010,
%T A079267 610,120,15,1,47844,51499,25914,7980,1645,231,21,1
%N A079267 d(n,s) = number of perfect matchings on {1, 2, ..., n} with k short pairs.
%C A079267 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.
%D A079267 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
%D A079267 J. L. Martin, The slopes determined by n points in the plane, preprint, 
               2003.
%H A079267 J. L. Martin, <a href="http://www.math.umn.edu/~martin/math/slopes.pdf">
               The slopes determined by n points in the plane</a>.
%F A079267 d(n, s) = 1/s! * sum(((-1)^(h-s)*(2*n-h)!/(2^(n-h)*(n-h)!*(h-s)!)), h=s..n)
%F A079267 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]
%e A079267 Triangle begins:
%e A079267 1
%e A079267 0 1
%e A079267 1 1 1
%e A079267 5 6 3 1
%e A079267 36 41 21 6 1
%p A079267 d := (n,s) -> 1/s! * sum('((-1)^(h-s)*(2*n-h)!/(2^(n-h)*(n-h)!*(h-s)!))',
               'h'=s..n):
%Y A079267 Row sums are A001147. Columns are A000806, A006198, A006199, A006200.
%Y A079267 Sequence in context: A018851 A011499 A106599 this_sequence A060296 A152061 
               A114598
%Y A079267 Adjacent sequences: A079264 A079265 A079266 this_sequence A079268 A079269 
               A079270
%K A079267 easy,nice,nonn,tabl
%O A079267 0,7
%A A079267 Jeremy Martin (martin(AT)math.umn.edu), Feb 05 2003

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