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 A035319 Number of rooted maps of genus n with one vertex and one face; the maps are considered on orientable surfaces and contain 2n edges. 8
 1, 1, 21, 1485, 225225, 59520825, 24325703325, 14230536445125, 11288163762500625, 11665426077721040625, 15230046989184655753125, 24515740420894935215128125, 47702727710977364941596305625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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 LINKS Gheorghe Coserea, Table of n, a(n) for n = 0..200 Nikita Alexeev and Peter Zograf, Hultman numbers, polygon gluings and matrix integrals, arXiv preprint arXiv:1111.3061 [math.PR], 2011. J.-P. Doignon and A. Labarre, On Hultman Numbers, J. Integer Seq., 10 (2007), 13 pages. T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus. I, J. Comb. Theory B 13 (1972), 192-218 (Tab.1). FORMULA a(n) = A035318(2*n). - Valery A. Liskovets, Apr 13 2006 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 a(n) = (4n)!/(2^(2n)(2n+1)!) = (4n-1)!!/(2n+1) = A001147(2n)/(2n+1). - Valery A. Liskovets, Apr 13 2006 MAPLE A035319 := proc(n) (4*n)!/4^n/(2*n+1)! ; end proc: seq(A035319(n), n=0..10) ; # R. J. Mathar, Jun 12 2018 PROG (PARI) a(n) = (4*n)!/((2*n+1)!*4^n); \\ Gheorghe Coserea, Jan 21 2017 CROSSREFS Right-hand diagonal of A035309. Cf. A035309. Sequence in context: A298851 A118446 A130332 * A278323 A301432 A220561 Adjacent sequences: A035316 A035317 A035318 * A035320 A035321 A035322 KEYWORD nonn AUTHOR N. J. A. Sloane EXTENSIONS More terms from Valery A. Liskovets, Apr 13 2006 STATUS approved

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Last modified November 30 01:30 EST 2023. Contains 367452 sequences. (Running on oeis4.)