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Search: id:A100898
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| A100898 |
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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). |
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+0
1
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| 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; listen)
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OFFSET
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0,5
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COMMENT
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Row n contains 1+ceil(n/2) terms. The row sums yield A029907.
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FORMULA
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G.f.=(1-z)(1+tz)/(1-z-tz^2)^2.
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EXAMPLE
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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;
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MAPLE
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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
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CROSSREFS
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Cf. A029907.
Adjacent sequences: A100895 A100896 A100897 this_sequence A100899 A100900 A100901
Sequence in context: A131032 A130323 A130303 this_sequence A101350 A134867 A102573
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KEYWORD
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nonn,tabf
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 10 2005
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