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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.
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
Sequence in context: A300202 A347107 A138323 * A303415 A301401 A162132
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

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