cp's OEIS Frontend

A214817 Number of genus 2 rooted hypermaps with n darts.

%I A214817 #61 Aug 23 2022 14:02:31
%S A214817 0,0,0,0,8,252,4956,77992,1074564,13545216,160174960,1805010948,
%T A214817 19588944336,206254571236,2118399516180,21310566266640,
%U A214817 210636265153004,2050696768165560,19704531058696008,187168609978022860,1759888050471704664,16398685297890141180,151570887948878270348
%N A214817 Number of genus 2 rooted hypermaps with n darts.
%C A214817 The table in the Zograf paper has an incorrect value for a(14). - _Gheorghe Coserea_, Nov 11 2018
%H A214817 Gheorghe Coserea, <a href="/A214817/b214817.txt">Table of n, a(n) for n = 1..105</a> (corrected by _Georg Fischer_, Jan 20 2019)
%H A214817 Mednykh, A.; Nedela, R. <a href="https://doi.org/10.1007/s10958-017-3555-5">Recent progress in enumeration of hypermaps</a>,  J. Math. Sci., New York 226, No. 5, 635-654 (2017) and Zap. Nauchn. Semin. POMI 446, 139-164 (2016), table 4.
%H A214817 Timothy R. Walsh, <a href="http://www.info2.uqam.ca/~walsh_t/papers/GENERATING NONISOMORPHIC.pdf">Space-efficient generation of nonisomorphic maps and hypermaps</a>
%H A214817 T. R. Walsh, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Walsh/walsh3.html">Space-Efficient Generation of Nonisomorphic Maps and Hypermaps</a>, J. Int. Seq. 18 (2015) # 15.4.3.
%H A214817 P. G. Zograf, <a href="https://doi.org/10.1093/imrn/rnv077">Enumeration of Grothendieck's Dessins and KP Hierarchy</a>, International Mathematics Research Notices, Volume 2015, Issue 24, 1 January 2015, 13533-13544.
%H A214817 Peter Zograf, <a href="https://arxiv.org/abs/1312.2538">Enumeration of Grothendieck's Dessins and KP Hierarchy</a>, arXiv:1312.2538 [math.CO], 2014.
%F A214817 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
%t A214817 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 *)
%o A214817 (PARI)
%o A214817 seq(N) = {
%o A214817   my(x='x+O('x^(N+2)), y=(1-sqrt(1-8*x))/(4*x));
%o A214817   Vec(-y*(y - 1)^5*(y^4 - 6*y^3 + 36*y^2 - 50*y + 51)/(4*(y - 2)^7*(y + 1)^5));
%o A214817 };
%o A214817 seq(19) \\ _Gheorghe Coserea_, Nov 11 2018
%Y A214817 Cf. A000108, A000257, A118093, A214817, A214818, A003319.
%K A214817 nonn
%O A214817 1,5
%A A214817 _N. J. A. Sloane_, Jul 31 2012
%E A214817 a(13) by _Noam Zeilberger_, Sep 16 2018
%E A214817 More terms and a(14) corrected by _Gheorghe Coserea_, Nov 11 2018