This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A000184 M2128 N0843 #51 Jan 19 2025 00:34:43
%S A000184 2,22,164,1030,5868,31388,160648,795846,3845020,18211380,84876152,
%T A000184 390331292,1775032504,7995075960,35715205136,158401506118,
%U A000184 698102372988,3059470021316,13341467466520,57918065919924,250419305769512,1078769490401032,4631680461623664,19825379450255900,84622558822506328,360270317908904328,1530148541536781488,6484511936352543096,27423786092731382000,115756362341775227888
%N A000184 Number of genus 0 rooted maps with 3 faces with n vertices.
%D A000184 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000184 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A000184 T. R. S. Walsh, Combinatorial Enumeration of Non-Planar Maps. Ph.D. Dissertation, Univ. of Toronto, 1971.
%H A000184 Alois P. Heinz, <a href="/A000184/b000184.txt">Table of n, a(n) for n = 2..500</a>
%H A000184 Richard P. Stanley, <a href="http://www-math.mit.edu/~rstan/ec/catadd.pdf">CATALAN ADDENDUM</a>, version of Jul 19, 2008, p. 24. [From _Jonathan Vos Post_, Aug 16 2008]
%H A000184 M. S. Tokmachev, <a href="https://vestnik.susu.ru/mmph/article/viewFile/8337/6806">Correlations Between Elements and Sequences in a Numerical Prism</a>, Bulletin of the South Ural State University, Ser. Mathematics. Mechanics. Physics, 2019, Vol. 11, No. 1, 24-33.
%H A000184 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 A000184 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 A000184 <a href="/A007401/a007401_1.pdf">Notes</a>
%F A000184 a(n) = 2 * A029887(n-2). - _Ralf Stephan_, Aug 17 2004
%F A000184 a(n) = 4^n*Gamma(n+3/2)/(3*sqrt(Pi)*Gamma(n)) - n*4^(n-1). - _Mark van Hoeij_, Jul 06 2010
%F A000184 From _G. C. Greubel_, Jul 18 2024: (Start)
%F A000184 a(n) = (n/12)*( (n+1)*(n+2)*Catalan(n+1) - 3*4^n ).
%F A000184 G.f.: x*(1 - sqrt(1 - 4*x))/(1-4*x)^(5/2).
%F A000184 E.g.f.: (x/3)*exp(2*x)*( - 3*exp(2*x) + 3*(1+2*x)*BesselI(0, 2*x) + (3+8*x)*BesselI(1, 2*x) + 2*x*BesselI(2, 2*x) ). (End)
%t A000184 a[n_] := 1/12*(2^(n+1)*(2*n+1)!!/(n-1)!-3*4^n*n); Table[a[n], {n, 2, 31}] (* _Jean-François Alcover_, Mar 12 2014 *)
%o A000184 (Magma)
%o A000184 [n*((n+1)*(n+2)*Catalan(n+1) - 3*4^n)/12: n in [2..30]]; // _G. C. Greubel_, Jul 18 2024
%o A000184 (SageMath)
%o A000184 [n*(2*(2*n+1)*binomial(2*n,n) - 3*4^n)//12 for n in range(2,30)] # _G. C. Greubel_, Jul 18 2024
%Y A000184 Column 3 of A269920.
%Y A000184 Column 0 of A270407.
%Y A000184 Cf. A000108, A029887.
%K A000184 nonn
%O A000184 2,1
%A A000184 _N. J. A. Sloane_
%E A000184 More terms from _Sean A. Irvine_, Nov 14 2010