

A000184


Number of genus 0 rooted maps with 3 faces with n vertices.
(Formerly M2128 N0843)


4



2, 22, 164, 1030, 5868, 31388, 160648, 795846, 3845020, 18211380, 84876152, 390331292, 1775032504, 7995075960, 35715205136, 158401506118, 698102372988, 3059470021316, 13341467466520, 57918065919924, 250419305769512, 1078769490401032, 4631680461623664, 19825379450255900, 84622558822506328, 360270317908904328, 1530148541536781488, 6484511936352543096, 27423786092731382000, 115756362341775227888
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OFFSET

2,1


REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
T. R. S. Walsh, Combinatorial Enumeration of NonPlanar Maps. Ph.D. Dissertation, Univ. of Toronto, 1971.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 2..500
Richard P. Stanley, CATALAN ADDENDUM, version of Jul 19, 2008, p. 24. [From Jonathan Vos Post, Aug 16 2008]
M. S. Tokmachev, Correlations Between Elements and Sequences in a Numerical Prism, Bulletin of the South Ural State University, Ser. Mathematics. Mechanics. Physics, 2019, Vol. 11, No. 1, 2433.
W. T. Tutte, On the enumeration of planar maps, Bull. Amer. Math. Soc. 74 1968 6474.
T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus, J. Comb. Thy B13 (1972), 122141 and 192218.
Notes


FORMULA

Appears to be 2 * A029887(n).  Ralf Stephan, Aug 17 2004
a(n) = 4^n*GAMMA(n+3/2)/(3*sqrt(Pi)*GAMMA(n))  n*4^(n1).  Mark van Hoeij, Jul 06 2010


MATHEMATICA

a[n_] := 1/12*(2^(n+1)*(2*n+1)!!/(n1)!3*4^n*n); Table[a[n], {n, 2, 31}] (* JeanFrançois Alcover, Mar 12 2014 *)


CROSSREFS

Sequence in context: A279380 A230835 A270407 * A007613 A279801 A043037
Adjacent sequences: A000181 A000182 A000183 * A000185 A000186 A000187


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Sean A. Irvine, Nov 14 2010


STATUS

approved



