0,4

First differences of central binomial coefficients: a(n)=A001405(n+1)-A001405(n).

The maximum size of an intersecting (or proper) antichain on an n-set - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 27 2000

Number of ordered trees with n+1 edges, having root of degree at least 2 and nonroot nodes of outdegree 0 or 2. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 02 2002

a(n)=number of Dyck (n+1)-paths that are symmetric but not prime. A prime Dyck path is one that returns to the x-axis only at its terminal point. For example a(3)=3 counts UDUUDDUD, UUDDUUDD, UDUDUDUD. - David Callan (callan(AT)stat.wisc.edu), Dec 09 2004

Number of involutions of [n+2] containing the pattern 132 exactly once. For example, a(3)=3 because we have 1'3'2'45, 42'5'13' and 52'4'3'1 (the entries corresponding to the pattern 132 are "primed"). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 17 2005

Also number of ways to put n eggs in floor(n/2) baskets where order of the baskets matters and all baskets have at least 1 egg. - Ben Thurston (benthurston27(AT)yahoo.com), Sep 30 2006

[1,1,3,4,10,15,35,56,...] is the convolution of A001405 with A126120 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 17 2007

M. van der Vel, Determination of msd(L^n), J. Algebraic Combin., 9 (1999), 161-171.

E. Deutsch, Ordered trees with prescribed root degrees, node degrees and branch lengths, Discrete Math., 282, 2004, 89-94.

O. Guibert and T. Mansour, Restricted 132-involutions, Sem. Lotharingien de Combinatoire, 48, 2002, Article B48a (Corollary 4.2).

E.g.f.: BesselI(1, 2*x)+BesselI(2, 2*x). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 28 2003

O.g.f.: [1-sqrt(1-4x^2)]/[x-2x^2+x*sqrt(1-4x^2)].

Cf. A032263, A051303-A051307, A001405.

Cf. A047171, A036256, A051920.

Sequence in context: A055720 A054184 A007007 this_sequence A093512 A081160 A051437

Adjacent sequences: A037949 A037950 A037951 this_sequence A037953 A037954 A037955

nonn

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