OFFSET
0,5
COMMENTS
Row n contains 1 + ceiling(n/2) terms. The row sums yield A029907.
FORMULA
G.f.: (1-z)(1+t*z)/(1 - z - t*z^2)^2.
EXAMPLE
T(3,2)=2 because in the graph with vertex set {O,A,B,C} and edge set {AB,BC,OA,OB,OC} the 2-matchings are: {OA,BC} and {OC,AB}.
The triangle starts:
1;
1, 1;
1, 3;
1, 5, 2;
1, 7, 7;
1, 9, 15, 3;
1, 11, 26, 13;
MAPLE
G:=(1-z)*(1+t*z)/(1-z-t*z^2)^2:Gser:=simplify(series(G, z=0, 18)):P[0]:=1: for n from 1 to 16 do P[n]:=sort(coeff(Gser, z^n)) od:for n from 0 to 15 do seq(coeff(t*P[n], t^k), k=1..1+ceil(n/2)) od; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Jan 10 2005
STATUS
approved