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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 (list; graph; refs; listen; history; text; internal format)
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 Non-Planar 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]

Tutte, W. T.; On the enumeration of planar maps. Bull. Amer. Math. Soc. 74 1968 64-74.

T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus, J. Comb. Thy B13 (1972), 122-141 and 192-218.

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^(n-1). - Mark van Hoeij, Jul 06 2010

MATHEMATICA

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 *)

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

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Last modified March 23 19:17 EDT 2017. Contains 283957 sequences.