1,3

Also, number of even minus number of odd extensions of truncated n-1 by n grid diagram.

Also, a(n) is the degree of the spinor variety, the complex projective variety SO(2n+1)/U(n). See Hiller's paper. - Burt Totaro (b.totaro(AT)dpmms.cam.ac.uk), Oct 29 2002

Also, number of ways of placing 1,...,n in a triangular array such that both rows and columns are increasing. - Jon Perry (perry(AT)globalnet.co.uk), Jun 13 2003

E.g. a(3)=2 as we can write:

1

23

456

or

1

24

356

Also, the number of symbolic sequences on the n symbols 0,1, ..., n-1. A symbolic sequence is a sequence that has n occurrences of 0, n-1 occurrences of 1, ..., one occurrence of n-1 and satisfies the condition that between any two consecutive occurrences of the symbol i it has exactly one occurrence of the symbol i+1. For example, the two symbolic sequences on 3 symbols are 012010 and 010210. The Shapiro-Shapiro paper shows how such sequences arise in the study of the arrangement of the real roots of a polynomial and its derivatives. There is a natural bijection between symbolic sequences and the triangular arrays described above. - Peter Bala (pbala(AT)toucansurf.com), Jul 18 2007

D. E. Barton and C. L. Mallows, Some aspects of the random sequence, Ann. Math. Statist. 36 (1965) 236-260.

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. M. Thrall, A combinatorial problem, Michigan Math. J. 1, (1952), 81-88.

D. E. Barton and C. L. Mallows, Some aspects of the random sequence, Ann. Math. Statist. 36 (1965) 236-260.

F. Ruskey, Generating linear extensions of posets by transpositions, J. Combin. Theory, B 54 (1992), 77-101.

B. Shapiro and M. Shapiro, A few riddles behind Rolle's theorem

R. M. Thrall, A combinatorial problem, Michigan Math. J. 1, (1952), 81-88.

Dennis White, Sign-balanced posets

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

(PARI) a(n)=((n*n+n)/2)!*prod(i=1, n, (i-1)!/(2*i-1)!)

Cf. A005118, A018241, A007724, A004065.

Cf. A131811.

Adjacent sequences: A003118 A003119 A003120 this_sequence A003122 A003123 A003124

Sequence in context: A012444 A012754 A083568 this_sequence A057170 A008338 A000178

nonn,nice,easy

C. L. Mallows (colinm(AT)research.avayalabs.com)

More terms from Michael Somos . Additional references from Frank Ruskey (fruskey(AT)cs.uvic.ca)