1,2

Also total number of blocks of odd size in all Catalan(n) possible noncrossing partitions of [n].

Convolution of the sequence of central binomial coefficients 1,2,6,20,70,... (A000984) and of the sequence of Fine numbers 1,0,1,2,6,18,... (A000957).

Row sums of A119307. - Paul Barry (pbarry(AT)wit.ie), May 13 2006

Paul Barry, A Catalan Transform and Related Transformations on Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.

N. Dershowitz and S. Zaks, Ordered trees and non-crossing partitions, Discrete Math., 62 (1986), 215-218.

E. Deutsch and L. Shapiro, A survey of the Fine numbers, Discrete Math., 241 (2001), 241-265.

Index entries for sequences related to rooted trees

2*binomial(2*n-1, n)/3 + A000957(n)/3;

Sum_{k=0..n} (-1)^(n-k)*binomial(n+k-1, k-1). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 28 2002

G.f.: 2z/[1-4z+(1+2z)sqrt(1-4z)].

a(n)=sum(binomial(2n-2j-2, n-1), j=0..floor((n-1)/2)).

2*a(n) + a(n-1)=(3*n-1)*Catalan(n-1). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Dec 03 2004

a(n)=(-1)^n*sum(i=0, n, sum(j=n, 2*n, (-1)^(i+j)*binomial(j, i))) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 18 2005

a(n)=sum{k=0..n, C(2k,n)} [offset 0]. - Paul Barry (pbarry(AT)wit.ie), May 13 2006

a(n)=sum{k=0..n, (-1)^(n-k)*C(n+k-1,k-1)}; - Paul Barry (pbarry(AT)wit.ie), Jul 18 2006

sum(igcd(binomial(2*j,n)),j=0..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 25 2006

a:=n->sum(igcd(binomial(2*j, n)), j=0..n): seq(a(n), n=0..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 25 2006

Cf. A059481.

Cf. A000957, A000984.

Sequence in context: A052986 A053368 A141753 this_sequence A128086 A131824 A104625

Adjacent sequences: A014297 A014298 A014299 this_sequence A014301 A014302 A014303

nonn,nice,easy

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