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Search: id:A035319
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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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+0
3
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| 1, 1, 21, 1485, 225225, 59520825, 24325703325, 14230536445125, 11288163762500625, 11665426077721040625, 15230046989184655753125, 24515740420894935215128125, 47702727710977364941596305625
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Even bisection of A035318. - Valery A. Liskovets (liskov(AT)im.bas-net.by), Apr 13 2006
a(n) is also the number of 2-permutations in Sym(4n-1), for n>1 (see Doignon and Labarre). - Anthony Labarre (alabarre(AT)ulb.ac.be), Jun 19 2007
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REFERENCES
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T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus. I, J. Comb. Theory, B, 13, No.3 (1972), 192-218 (Tab.1).
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LINKS
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J.-P. Doignon and A. Labarre, On Hultman Numbers, J. Integer Seq., 10 (2007), 13 pages.
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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 showed up - 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
a(n)=(4n)!/(2^{2n}(2n+1)!)=(4n-1)!!/(2n+1)=A001147(2n)/(2n+1). - Valery A. Liskovets (liskov(AT)im.bas-net.by), Apr 13 2006
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CROSSREFS
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Right-hand diagonal of A035309.
Cf. A035309.
Sequence in context: A036519 A118446 A130332 this_sequence A081786 A130039 A007593
Adjacent sequences: A035316 A035317 A035318 this_sequence A035320 A035321 A035322
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KEYWORD
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nonn
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AUTHOR
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njas
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EXTENSIONS
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More terms from Valery A. Liskovets (liskov(AT)im.bas-net.by), Apr 13 2006
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