0,2

Number of underdiagonal lattice paths from (0,0) to the line x=n, using only steps R=(1,0), V=(0,1) and D=(1,2). Also number of Motzkin paths of length n in which both the "up" and the "level" steps come in two colors. E.g. a(2)=6 because we have RR, RVR, RRV, RD, RVRV, and RRVV. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 21 2003

Inverse binomial transform of little Schroeder numbers 1,3,11... (A001003 with first term deleted) - David Callan (callan(AT)stat.wisc.edu), Feb 07 2004

a(n) is the number of planar trees satisfying: 1) Every internal node has at least two children, 2) Among the children of a node, only the leftmost and the rightmost children can be leaves, 3) The tree has n+1 leaves. For instance a(3)=6. - Marcelo Aguiar (maguiar(AT)math.tamu.edu), Oct 14 2005

Hankel transform is A006125(n+1)=2^C(n+1,2). - Paul Barry (pbarry(AT)wit.ie), Jan 08 2008

D. Merlini, D. G. Rogers, R. Sprugnoli and M. C. Verri, On some alternative characterizations of Riordan arrays, Canad. J. Math., 49 (1997), 301-320.

D. Merlini, D. G. Rogers, R. Sprugnoli and M. C. Verri, On some alternative characterizations of Riordan arrays, Canad. J. Math., 49 (1997), 301-320.

Marcelo Aguiar and Walter Moreira, Combinatorics of the free Baxter algebra, see Corollary 3.3.iii.

G.f. A(x) satisfies 2x^2A(x)^2+(2x-1)A(x)+1=0 and A(x)=1/(1-2x-2x^2/A(x)). - Michael Somos, Sep 06 2003

a(n)=sum{k=0..floor(n/2), C(n, 2k)C(k)2^(n-2k)*2^k}; - Paul Barry (pbarry(AT)wit.ie), May 18 2005

G.f.: (1 -2*x -sqrt(1 -4*x -4*x^2) )/(4*x^2) = 2/(1 -2*x +sqrt(1 -4*x -4*x^2)) .

Moment representation is a(n)=(1/(4*pi))*int(x^n*sqrt(4-4x-x^2),x,-2*sqrt(2)-2,2*sqrt(2)-2); - Paul Barry (pbarry(AT)wit.ie), Jan 08 2008

seq (ceil((sum(binomial(n, j)*binomial(2*j, n-1)/n, j=1..n))/2), n=1..25); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 10 2007

(PARI) a(n)=if(n<0, 0, n++; polcoeff(serreverse(x/(1+2*x+2*x^2)+x*O(x^n)), n))

(PARI) {a(n)= if(n<1, n==0, polcoeff( 2/(1 -2*x +sqrt(1 -4*x -4*x^2 +x*O(x^n))), n))}

(PARI) {a(n)= local(A); if(n<0, 0, A= x*O(x^n); n!*simplify(polcoeff( exp(2*x +A)* besseli(1, 2*x* quadgen(8) +A), n)))} /* Michael Somos Mar 31 2007 */

A036774(n)=a(n-1)n!/2^(n-1).

Row sums of A071943.

Sequence in context: A049129 A063376 A049139 this_sequence A141200 A122737 A059279

Adjacent sequences: A071353 A071354 A071355 this_sequence A071357 A071358 A071359

nonn

njas, Jun 12 2002