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A006295 Number of genus 1 rooted maps with 2 faces with n vertices
(Formerly M4739)
2
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).

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

LINKS

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

W. T. Tutte, 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

G.f.: x(1-sqrt(1-4*x))(11+12*x+9*sqrt(1-4*x))/(4(4*x-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 June 29 00:57 EDT 2016. Contains 274290 sequences.