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Search: id:A089436
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| A089436 |
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Number of non-crossing connected graphs on n nodes on a circle in which a fixed (distinguished) node has degree one. |
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+0
1
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| 1, 2, 9, 54, 374, 2820, 22485, 186494, 1592778, 13914108, 123750874, 1116809628, 10201516332, 94140605832, 876332565837, 8219124900558, 77594375595266, 736785675010380, 7031930543228910, 67420537625021460, 649070964647075700
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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Convolution of (1, A007297) with itself.
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REFERENCES
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P. Flajolet and M. Noy, Analytic combinatorics of non-crossing configurations, Discrete Math. 204 (1999), 203-229.
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FORMULA
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G.f.=g^2, where g satisfies g^3+g^2-3zg+2z^2=0, g(0)=0, or, in Maple notation, g := -1/3+(2/3)*sqrt(1+9*z)*sin((1/3)*arcsin((2+27*z+54*z^2)/2/(1+9*z)^(3/2))).
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EXAMPLE
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a(3)=2 because among the four non-crossing graphs on the points A,B,C, the distinguished node A has degree equal to 1 only in the graphs {AB,BC} and {AC,BC}; in the other two graphs ({AB,AC} and {AB,BC,AC}) the node A has degree 2.
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CROSSREFS
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Cf. A007297.
Adjacent sequences: A089433 A089434 A089435 this_sequence A089437 A089438 A089439
Sequence in context: A080146 A074602 A073986 this_sequence A000168 A127128 A064151
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 28 2003
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