OFFSET
0,4
COMMENTS
FORMULA
G.f.=G=1/(1-z+tz-tzR), where R=[1-z-sqrt(1-6z+z^2)]/(2z) is the g.f. of the large Schroeder numbers (A006318).
EXAMPLE
T(4,2)=4 because we have UUD(D)UUD(D),UUD(D)UH(D),UH(D)UUD(D) and UH(D)UH(D), where U=(1,1), D=(1,-1) and H=(2,0) (the returns to the x-axis are shown between parentheses).
Triangle starts:
1;
1;
1,2;
1,10;
1,40,4;
1,160,36;
MAPLE
R:=(1-z-sqrt(1-6*z+z^2))/2/z: G:=1/(1-z+t*z-t*z*R): Gser:=simplify(series(G, z=0, 16)): P[0]:=1: for n from 1 to 13 do P[n]:=coeff(Gser, z^n) od: for n from 0 to 13 do seq(coeff(t*P[n], t^j), j=1..1+floor(n/2)) od; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Dec 26 2005
STATUS
approved