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A006295 Number of genus 1 rooted maps with 2 faces with n vertices
(Formerly M4739)
0
10, 167, 1720, 14065, 100156, 649950, 3944928, 22764165, 126264820, 678405090, 3550829360, 18182708362, 91392185080, 452077562620, 2205359390592, 10627956019245, 50668344988068, 239250231713210, 1120028580999440, 5202779260636958, 23998704563581000, 109991785264412452, 501177338394193600, 2271383798432172450, 10243348296746854536, 45984242301056376660, 205559341637958057568, 915285296612144724660, 4060537494602836978160, 17952439453856255549176, 79117286081659327659520 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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

T. R. S. Walsh, Combinatorial Enumeration of Non-Planar Maps. Ph.D. Dissertation, Univ. of Toronto, 1971.

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

LINKS

Table of n, a(n) for n=3..33.

FORMULA

G.f.: x(1-sqrt(1-4x))(11+12x+9sqrt(1-4x))/(4(4x-1)^4)

CROSSREFS

Sequence in context: A054688 A229228 A112650 * A006297 A099711 A203532

Adjacent sequences:  A006292 A006293 A006294 * A006296 A006297 A006298

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms and g.f. from Sean A. Irvine, Nov 14 2010

STATUS

approved

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Last modified December 22 08:33 EST 2014. Contains 252329 sequences.