

A100898


Triangle read by rows: T(n,k) is the number of kmatchings of the fan graph on n+1 vertices (i.e., the join of the path graph on n vertices with one extra vertex).


0



1, 1, 1, 1, 3, 1, 5, 2, 1, 7, 7, 1, 9, 15, 3, 1, 11, 26, 13, 1, 13, 40, 34, 4, 1, 15, 57, 70, 21, 1, 17, 77, 125, 65, 5, 1, 19, 100, 203, 155, 31, 1, 21, 126, 308, 315, 111, 6, 1, 23, 155, 444, 574, 301, 43, 1, 25, 187, 615, 966, 686, 175, 7, 1, 27, 222, 825, 1530, 1386, 532, 57
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OFFSET

0,5


COMMENTS

Row n contains 1 + ceiling(n/2) terms. The row sums yield A029907.


LINKS

Table of n, a(n) for n=0..70.


FORMULA

G.f.: (1z)(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 2matchings 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:=(1z)*(1+t*z)/(1zt*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

Cf. A029907.
Sequence in context: A131032 A130323 A130303 * A101350 A199478 A134867
Adjacent sequences: A100895 A100896 A100897 * A100899 A100900 A100901


KEYWORD

nonn,tabf


AUTHOR

Emeric Deutsch, Jan 10 2005


STATUS

approved



