%I M4739 #32 Dec 14 2017 21:22:50
%S 10,167,1720,14065,100156,649950,3944928,22764165,126264820,678405090,
%T 3550829360,18182708362,91392185080,452077562620,2205359390592,
%U 10627956019245,50668344988068,239250231713210,1120028580999440,5202779260636958,23998704563581000,109991785264412452,501177338394193600,2271383798432172450,10243348296746854536,45984242301056376660,205559341637958057568,915285296612144724660,4060537494602836978160,17952439453856255549176,79117286081659327659520
%N Number of genus 1 rooted maps with 2 faces with n vertices
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D T. R. S. Walsh, Combinatorial Enumeration of Non-Planar Maps. Ph.D. Dissertation, Univ. of Toronto, 1971.
%H Vincenzo Librandi, <a href="/A006295/b006295.txt">Table of n, a(n) for n = 3..1000</a>
%H W. T. Tutte, <a href="http://dx.doi.org/10.1090/S0002-9904-1968-11877-4">On the enumeration of planar maps</a>, Bull. Amer. Math. Soc. 74 1968 64-74.
%H T. R. S. Walsh and A. B. Lehman, <a href="http://dx.doi.org/10.1016/0095-8956(72)90056-1">Counting rooted maps by genus</a>, J. Comb. Thy B13 (1972), 122-141 and 192-218.
%H <a href="/A007401/a007401_1.pdf">Notes</a>
%F G.f.: x(1-sqrt(1-4*x))(11+12*x+9*sqrt(1-4*x))/(4(4*x-1)^4). - _Sean A. Irvine_, Nov 14 2010
%t Rest[CoefficientList[Series[(1 - Sqrt[1 - 4 x]) (11 + 12 x + 9 Sqrt[1 - 4 x]) / (4 (4 x - 1)^4), {x, 0, 40}], x]] (* _Vincenzo Librandi_, Jun 06 2017 *)
%o (PARI)
%o A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
%o A006295_ser(N) = {
%o my(y = A000108_ser(N+1)); y*(y-1)^3*(y^2 + 15*y - 6)/(y-2)^8;
%o };
%o Vec(A006295_ser(31)) \\ _Gheorghe Coserea_, Jun 04 2017
%o (PARI) x = 'x + O('x^60); Vec(x*(1-sqrt(1-4*x))*(11+12*x+9*sqrt(1-4*x))/(4*(4*x-1)^4)) \\ _Michel Marcus_, Jun 05 2017
%Y Rooted maps of genus 1 with n edges and f faces for 1<=f<=10: A002802(with offset 2) f=1, this sequence, A006296 f=3, A288071 f=4, A288072 f=5, A287046 f=6, A287047 f=7, A287048 f=8, A288073 f=9, A288074 f=10.
%Y Column 2 of A269921, column 1 of A270406.
%K nonn
%O 3,1
%A _N. J. A. Sloane_.
%E More terms from _Sean A. Irvine_, Nov 14 2010