OFFSET
0,2
COMMENTS
LINKS
Robert A. Sulanke, Objects Counted by the Central Delannoy Numbers, Journal of Integer Sequences, Volume 6, 2003, Article 03.1.5.
FORMULA
G.f.: (1-2tz+z+Q)/[1-3z-3tz-tz^2+2t^2*z^2+(1-tz)Q], where Q=sqrt(1-6z+z^2).
EXAMPLE
T(2,1)=6 because we have DNE, DEN, NED, END, NDE and EDN.
Triangle begins
1;
2,1;
6,6,1;
22,28,12,1;
90,130,80,20,1;
MAPLE
r:=(1-z-sqrt(1-6*z+z^2))/2/z: R:=1/(1-t*z-z*r): G:=1/(1-t*z-2*z*R): Gser:=simplify(series(G, z=0, 13)): P[0]:=1: for n from 1 to 10 do P[n]:=coeff(Gser, z^n) od: for n from 0 to 10 do seq(coeff(t*P[n], t^k), k=1..n+1) od; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Jul 14 2005
STATUS
approved