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A103940
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Number of unrooted bipartite n-edge maps in the plane (planar with a distinguished outside face).
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1
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1, 2, 5, 18, 72, 368, 1982, 11514, 69270, 430384, 2736894, 17752884, 117039548, 782480424, 5294705752, 36206357114, 249894328848, 1739030128872, 12191512867814, 86037243899240
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Bipartite planar maps are dual to Eulerian planar maps.
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REFERENCES
| V. A. Liskovets and T. R. Walsh, Enumeration of unrooted maps on the plane, Rapport technique, UQAM, No. 2005-01, Montreal, Canada, 2005.
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LINKS
| V. A. Liskovets and T. R. Walsh, Counting unrooted maps on the plane, Advances in Applied Math., 36, No.4 (2006), 364-387.
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FORMULA
| a(n)=(1/(2n))[2^(n-1)binomial(2n, n)/(n+1) + sum_{0<k<n, k|n}phi(n/k)d(n/k)2^(k-1)binomial(2k, k)]+q(n) where phi is the Euler function A000010, d(n)=2, q(n)=0 if n is even and d(n)=1, q(n)=2^((n-1)/2)binomial(n-1, (n-1)/2)/(n+1) if n is odd.
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CROSSREFS
| Cf. A003645, A103939, A069727.
Sequence in context: A141494 A189843 A045612 * A162543 A039744 A189281
Adjacent sequences: A103937 A103938 A103939 * A103941 A103942 A103943
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KEYWORD
| easy,nonn
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AUTHOR
| Valery A. Liskovets (liskov(AT)im.bas-net.by), Mar 17 2005
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