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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 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 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 November 30 06:18 EST 2022. Contains 358431 sequences. (Running on oeis4.)