The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A214817 Number of genus 2 rooted hypermaps with n darts. 5
 0, 0, 0, 0, 8, 252, 4956, 77992, 1074564, 13545216, 160174960, 1805010948, 19588944336, 206254571236, 2118399516180, 21310566266640, 210636265153004, 2050696768165560, 19704531058696008, 187168609978022860, 1759888050471704664, 16398685297890141180, 151570887948878270348 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS The table in the Zograf paper has an incorrect value for a(14). - Gheorghe Coserea, Nov 11 2018 LINKS Gheorghe Coserea, Table of n, a(n) for n = 1..105 (corrected by Georg Fischer, Jan 20 2019) Mednykh, A.; Nedela, R. Recent progress in enumeration of hypermaps, J. Math. Sci., New York 226, No. 5, 635-654 (2017) and Zap. Nauchn. Semin. POMI 446, 139-164 (2016), table 4. Timothy R. Walsh, Space-efficient generation of nonisomorphic maps and hypermaps T. R. Walsh, Space-Efficient Generation of Nonisomorphic Maps and Hypermaps, J. Int. Seq. 18 (2015) # 15.4.3. P. G. Zograf, Enumeration of Grothendieck's Dessins and KP Hierarchy, International Mathematics Research Notices, Volume 2015, Issue 24, 1 January 2015, 13533-13544. Peter Zograf, Enumeration of Grothendieck's Dessins and KP Hierarchy, arXiv:1312.2538 [math.CO], 2014. FORMULA G.f.: -y*(y - 1)^5*(y^4 - 6*y^3 + 36*y^2 - 50*y + 51)/(4*(y - 2)^7*(y + 1)^5), where y = C(2*x), C being the g.f. for A000108. - Gheorghe Coserea, Nov 11 2018 MATHEMATICA DeleteCases[CoefficientList[Series[-# (# - 1)^5*(#^4 - 6 #^3 + 36 #^2 - 50 # + 51)/(4 (# - 2)^7*(# + 1)^5) &[(1 - Sqrt[1 - 8 x])/(4 x)], {x, 0, 23}], x], 0] (* Michael De Vlieger, Nov 26 2018 *) PROG (PARI) seq(N) = { my(x='x+O('x^(N+2)), y=(1-sqrt(1-8*x))/(4*x)); Vec(-y*(y - 1)^5*(y^4 - 6*y^3 + 36*y^2 - 50*y + 51)/(4*(y - 2)^7*(y + 1)^5)); }; seq(19) \\ Gheorghe Coserea, Nov 11 2018 CROSSREFS Cf. A000108, A000257, A118093, A214817, A214818, A003319. Sequence in context: A300202 A347107 A138323 * A303415 A301401 A162132 Adjacent sequences: A214814 A214815 A214816 * A214818 A214819 A214820 KEYWORD nonn AUTHOR N. J. A. Sloane, Jul 31 2012 EXTENSIONS a(13) by Noam Zeilberger, Sep 16 2018 More terms and a(14) corrected by Gheorghe Coserea, Nov 11 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 13 23:31 EDT 2024. Contains 374290 sequences. (Running on oeis4.)