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A035319
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Number of rooted maps of genus n with one vertex and one face; the maps are considered on orientable surfaces and contain 2n edges.
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8
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1, 1, 21, 1485, 225225, 59520825, 24325703325, 14230536445125, 11288163762500625, 11665426077721040625, 15230046989184655753125, 24515740420894935215128125, 47702727710977364941596305625
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OFFSET
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0,3
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COMMENTS
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a(n) is also the number of 2-permutations in Sym(4n-1), for n>1 (see Doignon and Labarre). - Anthony Labarre, Jun 19 2007
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LINKS
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FORMULA
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It appears that this is given by the formula (4n)!/2^{2n}(2n+1)! = (4n-1)!!/(2n+1). (This sequence arose -- conjecturally, but it shouldn't be too hard to make it rigorous -- as the unique nontrivial Betti number of a certain poset associated to the hyperoctahedral group.) - Eric M. Rains (rains(AT)caltech.edu), Jan 24 2006
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MAPLE
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(4*n)!/4^n/(2*n+1)! ;
end proc:
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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