0,4

For n >= 2 by the hook length formula a(n) is also the number of Young tableaux of size 1+2+...+(n-1) = n(n-1)/2 that correspond to the partition (1,2,...n-1), i.e. triangular Young tableaux. For example when n=5 a(5)=768 and the shape of the tableau is xxxx / xxx / xx / x. - Ahmed Fares (ahmedfares(AT)my-deja.com), May 04 2001

Also, a(n) is the degree of the symplectic Grassmannian, the projective variety of all maximal isotropic subspaces in a complex vector space of dimension 2n-2 with a symplectic form. See Hiller's paper. - Burt Totaro (b.totaro(AT)dpmms.cam.ac.uk), Oct 29 2002

Also, for n >= 2, a(n) is the number of maximal chains in the poset of Dyck paths ordered by inclusion. - Jennifer Woodcock (Jennifer.Woodcock(AT)ugdsb.on.ca), May 21 2008

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, CRC Press, 1997, p. 102.

H. Hiller. Combinatorics and intersection of Schubert varieties. Comment. Math. Helv. 57 (1982), 41-59.

G. Kreweras, Sur un probleme de scrutin a plus de deux candidats, Publications de l'Institut de Statistique de l'Universit\'{e} de Paris, 26 (1981), 69-87.

R. P. Stanley, On the number of reduced decompositions of elements of certain groups, European J. Combin., 5 (1984), 359-372.

R. P. Stanley, A combinatorial miscellany

R. P. Stanley, Ordering events in Minkowski space

C(n, 2)!/(1^{n-1} * 3^{n-2} *...* (2n-3)^1 ).

a(n)=(n(n-1)/2)!/A057863(n-1) (n>=1). - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 21 2004

a(n) = A153452(A002110(n-1)). - Naohiro Nomoto, Jan 01 2009

A005118 := proc(n) local i; binomial(n, 2)!/product( (2*i+1)^(n-i-1), i=0..n-2 ); end;

Cf. A003121, A018241.

Cf. A057863.

Sequence in context: A012464 A128294 A015188 this_sequence A108400 A013029 A012915

Adjacent sequences: A005115 A005116 A005117 this_sequence A005119 A005120 A005121

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).