%I M5280 N2298 #31 Mar 28 2021 19:31:10
%S 42,1586,31388,442610,5030004,49145460,429166584,3435601554,
%T 25658464260,181055975100,1218601601672,7880146275092,49238911113224,
%U 298652277299880,1764885293279472,10192638073849554,57674223198273444,320430129184331628,1751190732477786600,9428906326013866076
%N Number of genus 0 rooted maps with 6 faces and n vertices.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%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 Andrew Howroyd, <a href="/A000502/b000502.txt">Table of n, a(n) for n = 5..500</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^4*(1-sqrt(1-4*x))*(105+92*x-(84+76*x)*sqrt(1-4*x))/(1-4*x)^7. - _Sean A. Irvine_, Nov 14 2010
%t CoefficientList[ x(1-Sqrt[1-4x])(105+92x-(84+76x)Sqrt[1-4x])/(1-4x)^7/x^2 + O[x]^30, x] (* _Jean-François Alcover_, Feb 09 2016 *)
%o (PARI) seq(n)={my(g=sqrt(1-4*x + O(x*x^n))); Vec((1-g)*(105+92*x - (84+76*x)*g)/((1-4*x)^7))} \\ _Andrew Howroyd_, Mar 28 2021
%Y Column 6 of A269920.
%Y Column 0 of A270410.
%K nonn
%O 5,1
%A _N. J. A. Sloane_
%E More terms from _Sean A. Irvine_, Nov 14 2010