A214817 Number of genus 2 rooted hypermaps with n darts.
0, 0, 0, 0, 8, 252, 4956, 77992, 1074564, 13545216, 160174960, 1805010948, 19588944336, 206254571236, 2118399516180, 21310566266640, 210636265153004, 2050696768165560, 19704531058696008, 187168609978022860, 1759888050471704664, 16398685297890141180, 151570887948878270348
Offset: 1
Keywords
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.
Programs
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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 *) -
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
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
Extensions
a(13) by Noam Zeilberger, Sep 16 2018
More terms and a(14) corrected by Gheorghe Coserea, Nov 11 2018
Comments