0,2

Number of leaves in all noncrossing rooted trees on n nodes on a circle.

Number of standard tableaux of shape (n-1,1^(2n-3)). - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 25 2004

a(n) = number of Dyck (2n-3)-paths with exactly one descent of odd length. For example, a(3) counts all 5 Dyck 3-paths except UDUDUD. - David Callan (callan(AT)stat.wisc.edu), Jul 25 2005

a(n+2) gives row sums of A119301. - Paul Barry (pbarry(AT)wit.ie), May 13 2006

Milan Janjic, Two Enumerative Functions

Index entries for sequences related to rooted trees

a(n) is asymptotic to c/sqrt(n)*(27/4)^n with c=0.73... - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 27 2003

G.f.: gz^2/(1-3zg^2), where g=g(z) is given by g=1+zg^3, g(0)=1, i.e. (in Maple command) g := 2*sin(arcsin(3*sqrt(3*z)/2)/3)/sqrt(3*z); - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 22 2003

a(n+2)=C(3n+1,n)=sum{k=0..n, C(3n-k,n-k)}; - Paul Barry (pbarry(AT)wit.ie), May 13 2006

a(n+2)=C(3n+1,2n+1)=A078812(2n,n); - Paul Barry (pbarry(AT)wit.ie), Nov 09 2006

[seq( binomial(3*n+1, n), n=0..40)]; - N. J. A. Sloane (njas(AT)research.att.com), Jun 09 2007

Sequence in context: A020048 A093426 A046090 this_sequence A101810 A001888 A103769

Adjacent sequences: A045718 A045719 A045720 this_sequence A045722 A045723 A045724

nonn

Emeric Deutsch (deutsch(AT)duke.poly.edu)

Simpler definition from Ira Gessel (gessel(AT)brandeis.edu), May 26 2007. This change means that most of the offsets in the comments will now need to be changed too.