0,2

a(n) = # Dyck (n+1)-paths all of whose components are symmetric. A strict Dyck path is one with exactly one return to ground level (necessarily at the end). Every nonempty Dyck path is expressible uniquely as a concatenation of one or more strict Dyck paths, called its components. - David Callan (callan(AT)stat.wisc.edu), Mar 02 2005

Inverse Chebyshev transform of the second kind applied to 2^n. This maps g(x)->c(x^2)g(xc(x^2)). - Paul Barry (pbarry(AT)wit.ie), Sep 14 2005

Hankel transform of this sequence gives A000012 = [1,1,1,1,1,1,1,...] . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 24 2007

Inverse binomial transform of A059738. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 24 2009]

J. W. Layman, The Hankel Transform and Some of its Properties, J. Integer Sequences, 4 (2001), #01.1.5.

a(n)= sum(A054336(n, m), m=0..n). G.f.: 1/(1-2*x-x^2*c(x^2)), where c(x) = g.f. for Catalan numbers A000108.

G.f.: c(x^2)/(1-2xc(x^2)); a(n)=sum{k=0..n, C(n, (n-k)/2)(1+(-1)^(n+k))2^k*(k+1)/(n+k+2)}. - Paul Barry (pbarry(AT)wit.ie), Sep 14 2005

a(n)=A127358(n+1)-2*A127358(n). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 02 2007

a(n)=A126075(n,0). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 24 2009]

a(n)= Sum_{k, 0<=k<=n} A053121(n,k)*2^k. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 28 2009]

Cf. A000108, A054336.

Sequence in context: A062423 A118649 A033482 this_sequence A000106 A076883 A140832

Adjacent sequences: A054338 A054339 A054340 this_sequence A054342 A054343 A054344

easy,nonn,new

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Mar 13 2000