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Search: id:A000356
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| A000356 |
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Number of rooted cubic maps with 2n nodes and a distinguished Hamilton cycle: (2n)!(2n+1)!/(n!^2*(n+1)!(n+2)!).
(Formerly M3978 N1647)
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+0
9
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| 1, 5, 35, 294, 2772, 28314, 306735, 3476330, 40831076, 493684828, 6114096716, 77266057400, 993420738000, 12964140630900, 171393565105575, 2291968851019650, 30961684478686500, 422056646314726500
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
W. T. Tutte, A census of Hamiltonian polygons, Canad. J. Math., 14 (1962), 402-417.
W. T. Tutte, On the enumeration of four-colored maps, SIAM J. Appl. Math., 17 (1969), 454-460.
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LINKS
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R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, J. Integer Seqs., Vol. 3 (2000), #00.1.6
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MAPLE
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f:=n->(2*n)!*(2*n+2)!/(2*n!*(n+1)!*(n+1)!*(n+2)!);
hypergeom([ 1, 5/2, 3/2 ], [ 3, 4 ], 16*x);
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CROSSREFS
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Cf. A000264, A000309.
Equals A005568/2.
Fourth row of array A102539.
Column of array A073165.
Image of A001700 under the "little Hankel" transform (see A056220 for definition) - John W. Layman (layman(AT)math.vt.edu), Aug 22 2000
Sequence in context: A138233 A002294 A051406 this_sequence A027392 A109253 A052797
Adjacent sequences: A000353 A000354 A000355 this_sequence A000357 A000358 A000359
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KEYWORD
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easy,nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
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Better definition from Michael Albert, Oct 24 2008
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