OFFSET
0,2
COMMENTS
FORMULA
G.f. = G(t,z) = (1-(1-t)z(1-z))/(1 - 3z + 2(1-t)z^2*(1-z)).
EXAMPLE
T(2,0)=5 because we have 00,11,12,21 and 22; T(2,1)=4 because we have 01,02,10 and 20; T(3,2)=2 because we have 010 and 020.
Triangle starts:
1;
2, 1;
5, 4;
13, 12, 2;
33, 36, 12;
83, 108, 48, 4;
MAPLE
G:=(1-(1-t)*z*(1-z))/(1-3*z+2*(1-t)*z^2*(1-z)): Gser:=simplify(series(G, z=0, 15)): P[0]:=1: for n from 1 to 13 do P[n]:=sort(coeff(Gser, z^n)) od: for n from 0 to 13 do seq(coeff(P[n], t, j), j=0..ceil(n/2)) od; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Jul 16 2006
STATUS
approved