OFFSET
0,3
COMMENTS
A Delannoy path of length n is a path from (0,0) to (n,n), consisting of steps E=(1,0), N=(0,1) and D=(1,1).
LINKS
Robert A. Sulanke, Objects Counted by the Central Delannoy Numbers, Journal of Integer Sequences, Volume 6, 2003, Article 03.1.5.
FORMULA
a(n) = sum(k*A110183(n,k),k=0..n).
G.f.: z(1-z-zr+z^2+z^2*r)/[(1-6z+z^2)(1-3z+z^2-zr+z^2*r)], where r=1+zr+zr^2=[1-z-sqrt(1-6z+z^2)]/(2z) is the g.f. of the large Schroeder numbers (A006318).
D-finite with recurrence n*a(n) +(-13*n+11)*a(n-1) +10*(5*n-9)*a(n-2) +10*(-5*n+16)*a(n-3) +(13*n-54)*a(n-4) +(-n+5)*a(n-5)=0. - R. J. Mathar, Jul 24 2022
EXAMPLE
MAPLE
r:=(1-z-sqrt(1-6*z+z^2))/2/z: G:=z*(1-z-z*r+z^2+z^2*r)/(1-6*z+z^2)/(1-3*z+z^2-z*r+z^2*r): Gser:=series(G, z=0, 27): 0, seq(coeff(Gser, z^n), n=1..24);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Jul 14 2005
STATUS
approved