OFFSET
2,4
COMMENTS
FORMULA
G.f.=G-1, where G=G(t, z) satisfies z(1+t+z)G^2-(1+z+tz)G+1=0.
EXAMPLE
T(5,2)=3 because we have UU(UD)DU(UD)DD, UUDU(UD)(UD)DD and UU(UD)(UD)DUDD, where U=(1,1), D=(1,-1) (the peaks at odd levels are shown between parentheses).
Triangle begins:
1;
1,1;
3,2,1;
6,8,3,1;
15,22,15,4,1;
MAPLE
G:=(t*z+z+1-sqrt(z^2*t^2+2*z^2*t-2*z*t-3*z^2-2*z+1))/2/z/(1+t+z)-1: Gser:=simplify(series(G, z=0, 15)): for n from 2 to 12 do P[n]:=coeff(Gser, z^n) od: for n from 2 to 12 do seq(coeff(t*P[n], t^j), j=1..n-1) od; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Dec 11 2005
STATUS
approved