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

1,5

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