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A143021
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Number of vertices of degree 1 in all non-crossing connected graphs on n points on a circle.
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0
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2, 6, 36, 270, 2244, 19740, 179880, 1678446, 15927780, 153055188, 1485010488, 14518525164, 142821228648, 1412109087480, 14021321053392, 139725123309486, 1396698760714788, 13998927825197220, 140638610864578200
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| a(n)=n*A089436(n).
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REFERENCES
| P. Flajolet and M. Noy, Analytic Combinatorics of Noncrossing Configurations, Discr. Math. 204 (1999), 203-229.
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FORMULA
| G.f.=z*diff(g^2,z), where g=g(z), the g.f. for the number of non-crossing connected graphs on n nodes on a circle, satisfies g^3 + g^2 -3zg +2z^2=0 (A007297).
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EXAMPLE
| a(3)=6 because in the graphs (AB,BC,CA), (AB,AC), (AB,BC) and (AC,BC) the vertices of degree 1 are: none, {B,C}, {A,C} and {A,B}.
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MAPLE
| g:=-1/3+(2/3)*sqrt(1+9*z)*sin((1/3)*arcsin(((2+27*z+54*z^2)*1/2)/(1+9*z)^(3/2))): ser:=series(z*(diff(g^2, z)), z=0, 25): seq(coeff(ser, z, n), n=2..21);
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CROSSREFS
| Cf. A007297, A089436.
Sequence in context: A096939 A162697 A107099 * A007657 A061302 A055541
Adjacent sequences: A143018 A143019 A143020 * A143022 A143023 A143024
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 30 2008
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