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%I M2128 N0843 #40 Mar 22 2019 00:30:03
%S 2,22,164,1030,5868,31388,160648,795846,3845020,18211380,84876152,
%T 390331292,1775032504,7995075960,35715205136,158401506118,
%U 698102372988,3059470021316,13341467466520,57918065919924,250419305769512,1078769490401032,4631680461623664,19825379450255900,84622558822506328,360270317908904328,1530148541536781488,6484511936352543096,27423786092731382000,115756362341775227888
%N Number of genus 0 rooted maps with 3 faces with 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 Alois P. Heinz, <a href="/A000184/b000184.txt">Table of n, a(n) for n = 2..500</a>
%H 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 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 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 Appears to be 2 * A029887(n). - _Ralf Stephan_, Aug 17 2004
%F a(n) = 4^n*GAMMA(n+3/2)/(3*sqrt(Pi)*GAMMA(n)) - n*4^(n-1). - _Mark van Hoeij_, Jul 06 2010
%t 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 *)
%K nonn
%O 2,1
%A _N. J. A. Sloane_
%E More terms from _Sean A. Irvine_, Nov 14 2010
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