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A000365 Number of genus 0 rooted planar maps with n vertices.
(Formerly M4022 N1669)
3
5, 93, 1030, 8885, 65954, 442610, 2762412, 16322085, 92400330, 505403910, 2687477780, 13957496098, 71053094420, 355548314180, 1752827693528, 8529176056965, 41026491589722, 195327793313790, 921451498774660, 4311086414580022, 20019238138410940 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

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).

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

T. D. Noe, Table of n, a(n) for n = 3..200

FORMULA

G.f.: x^2*(1-sqrt(1-4x))(7+4x-2sqrt(1-4x))/(2(4x-1)^4). - corrected for right offset by Vaclav Kotesovec, Aug 13 2013

a(n) ~ n^3*4^n/24 * (1-4/(sqrt(Pi*n))). - Vaclav Kotesovec, Aug 13 2013

MATHEMATICA

nn = 20; CoefficientList[Series[x^2 (1 - Sqrt[1 - 4 x]) (7 + 4 x - 2 Sqrt[1 - 4 x])/(2 (4 x - 1)^4), {x, 0, nn}], x] (* T. D. Noe, Jun 19 2012 *)

CROSSREFS

Sequence in context: A152283 A205344 A270408 * A209471 A012784 A015030

Adjacent sequences:  A000362 A000363 A000364 * A000366 A000367 A000368

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 November 21 12:51 EST 2017. Contains 295001 sequences.