OFFSET
1,2
COMMENTS
Row n contains n-1 terms (n>=2). Row sums are the little Schroeder numbers (A001003).
FORMULA
G.f.=G=z(t+H)/(1-z-zH), where H is given by H =z(2+H)(t+H).
EXAMPLE
T(3,2)=4 because we have (UH)D(H),(UU)DD(H),(UU)D(H)D and (UU)D(U)DD, where U=(1,1), D=(1,-1) and H=(2,0) (the weak ascents are shown between parentheses).
Triangle starts:
1;
3;
7,4;
15,26,4;
31,108,54,4;
MAPLE
H:=(1-z*t-2*z-sqrt(1-2*z*t-4*z+z^2*t^2-4*z^2*t+4*z^2))/2/z: G:=z*(t+H)/(1-z-z*H): Gser:=simplify(series(G, z=0, 15)): for n from 1 to 11 do P[n]:=coeff(Gser, z^n) od: 1; for n from 2 to 11 do seq(coeff(P[n], t^j), j=1..n-1) od; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Dec 24 2005
STATUS
approved