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A000473 Number of genus 0 rooted maps with 5 faces and n vertices.

%I A000473 M4953 N2122 #33 Mar 28 2021 19:31:01
%S A000473 14,386,5868,65954,614404,5030004,37460376,259477218,1697186964,
%T A000473 10596579708,63663115880,370293754740,2095108370600,11574690111400,
%U A000473 62629794691632,332742342741090,1739371969822260,8961709528660140,45576855706440520,229087231033907708
%N A000473 Number of genus 0 rooted maps with 5 faces and n vertices.
%D A000473 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000473 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A000473 T. R. S. Walsh, Combinatorial Enumeration of Non-Planar Maps. Ph.D. Dissertation, Univ. of Toronto, 1971.
%H A000473 Andrew Howroyd, <a href="/A000473/b000473.txt">Table of n, a(n) for n = 4..500</a>
%H A000473 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 A000473 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 A000473 <a href="/A007401/a007401_1.pdf">Notes</a>
%F A000473 G.f.: x^3*(1-sqrt(1-4*x))*(17+16*x-(10+4*x)*sqrt(1-4*x))/(1-4*x)^(11/2). - _Sean A. Irvine_, Nov 14 2010
%t A000473 CoefficientList[(1/x)(1-Sqrt[1-4x])(17+16x-(10+4x)Sqrt[1-4x])/(1-4x)^(11/2) + O[x]^36, x] (* _Jean-François Alcover_, Feb 08 2016 *)
%o A000473 (PARI) seq(n)={my(g=sqrt(1-4*x + O(x*x^n))); Vec((1-g)*(17+16*x-(10+4*x)*g)/((1-4*x)^5*g))} \\ _Andrew Howroyd_, Mar 28 2021
%Y A000473 Column 5 of A269920.
%Y A000473 Column 0 of A270409.
%K A000473 nonn
%O A000473 4,1
%A A000473 _N. J. A. Sloane_
%E A000473 More terms from _Sean A. Irvine_, Nov 14 2010