A214818 Number of genus 3 rooted hypermaps with n darts.

0, 0, 0, 0, 0, 0, 180, 9132, 268980, 6010220, 112868844, 1877530740, 28540603884, 404562365316, 5422718644920, 69428442576136, 855504181649448, 10204459810035768, 118364711625485256, 1340006035830921720, 14850353930248138104, 161502853638370415864, 1727146533728893094604

Offset

1,7

Links

Gheorghe Coserea, Table of n, a(n) for n = 1..107 (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 5

Timothy R. Walsh, Space-Efficient Generation of Nonisomorphic Maps and Hypermaps

Timothy R. Walsh, Space-Efficient Generation of Nonisomorphic Maps and Hypermaps, J. Int. Seq. 18 (2015) # 15.4.3.

Peter G. Zograf, Enumeration of Grothendieck's Dessins and KP Hierarchy, International Mathematics Research Notices, Volume 2015, Issue 24, 1 January 2015, 13533-13544.

Peter G. Zograf, Enumeration of Grothendieck's Dessins and KP Hierarchy, arXiv:1312.2538 [math.CO], 2014.

Formula

G.f.: y*(y - 1)^7*(5*y^9 - 60*y^8 + 675*y^7 - 2947*y^6 + 10005*y^5 - 20235*y^4 + 28297*y^3 - 23937*y^2 + 11418*y - 1781)/(2*(y - 2)^12*(y + 1)^9), where y = C(2*x), C being the g.f. for A000108. - Gheorghe Coserea, Nov 12 2018

Mathematica

DeleteCases[CoefficientList[Series[# (# - 1)^7*(5 #^9 - 60 #^8 + 675 #^7 - 2947 #^6 + 10005 #^5 - 20235 #^4 + 28297 #^3 - 23937 #^2 + 11418 # - 1781)/(2 (# - 2)^12*(# + 1)^9) &[(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)^7*(5*y^9 - 60*y^8 + 675*y^7 - 2947*y^6 + 10005*y^5 - 20235*y^4 + 28297*y^3 - 23937*y^2 + 11418*y - 1781)/(2*(y - 2)^12*(y + 1)^9));
};
seq(18) \\ Gheorghe Coserea, Nov 12 2018

Crossrefs

Cf. A000108, A000257, A118093, A214817, A003319.

Sequence in context: A243465 A271673 A008378 * A287022 A217791 A035830

Adjacent sequences: A214815 A214816 A214817 * A214819 A214820 A214821

Keyword

nonn

Author

N. J. A. Sloane, Aug 01 2012

Extensions

a(13)-a(14) by Noam Zeilberger, Sep 16 2018

More terms from Gheorghe Coserea, Nov 11 2018

Status

approved