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A006298
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Number of genus 2 rooted maps with 1 face with n vertices
(Formerly M5117)
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2
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21, 483, 6468, 66066, 570570, 4390386, 31039008, 205633428, 1293938646, 7808250450, 45510945480, 257611421340, 1422156202740, 7683009544980, 40729207226400, 212347275857640, 1090848505817070, 5530195966465170, 27704671055301240, 137308238124957900, 673903972248687180, 3278143051447003740, 15816495077491530240, 75740811006275677080, 360195962116311020700, 1702004224469594857812, 7994567449203067400976, 37343992994700814841496, 173539732151844963086952, 802554981295852197252840, 3694707104076119563303872, 16936911943685345325329616
(list; graph; refs; listen; history; internal format)
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OFFSET
| 4,1
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
T. R. S. Walsh, Combinatorial Enumeration of Non-Planar Maps. Ph.D. Dissertation, Univ. of Toronto, 1971.
T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus, J. Comb. Thy B13 (1972), 122-141 and 192-218.
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
| a(n+1) = ((5n+3)(4n+2)a(n))/((5n-2)(n-3))
G.f.: 21x^4(1+x)/sqrt[(1-x)^11]. a(n) = 21 * [A020922(n-4) + A020922(n-3)]. - R. Stephan, Mar 13 2004
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CROSSREFS
| Cf. A035309.
Sequence in context: A126996 A158603 A025603 * A089907 A015695 A006299
Adjacent sequences: A006295 A006296 A006297 * A006299 A006300 A006301
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from David W. Wilson (davidwwilson(AT)comcast.net)
More terms from Sean A. Irvine (sairvin(AT)xtra.co.nz), Nov 14 2010
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