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A100898 Triangle read by rows: T(n,k) is the number of k-matchings 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 (list; graph; refs; listen; history; text; internal format)
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.: (1-z)(1+tz)/(1 - z - tz^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

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

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Last modified July 10 14:17 EDT 2020. Contains 335576 sequences. (Running on oeis4.)