OFFSET
0,7
FORMULA
G.f.: 2(1 + (t-1)z(1-2z) + q(1 - z + tz))/((1-2z+q)(1+2z^2-2t^2*z^2+q)), where q = sqrt(1 - 4z^2).
EXAMPLE
T(5,2)=2 because we have uduududdud and uduuudddud, where u=(1,1), d=(1,-1).
Triangle begins:
1;
0, 1;
1, 0, 1;
2, 0, 0, 1;
4, 0, 1, 0, 1;
6, 1, 2, 0, 0, 1;
MAPLE
G:=-2*(z+z*sqrt(1-4*z^2)-2*z^2-z*t-1-sqrt(1-4*z^2)+2*z^2*t-z*t*sqrt(1-4*z^2))/(-1-sqrt(1-4*z^2)+2*z)/(-1-sqrt(1-4*z^2)-2*z^2+2*z^2*t^2): Gser:=simplify(series(G, z=0, 17)): 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^k), k=1..n+1) od; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Jun 17 2005
STATUS
approved