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A000473 Number of genus 0 rooted maps with 5 faces with n vertices.
(Formerly M4953 N2122)
1
14, 386, 5868, 65954, 614404, 5030004, 37460376, 259477218, 1697186964, 10596579708, 63663115880, 370293754740, 2095108370600, 11574690111400, 62629794691632, 332742342741090, 1739371969822260, 8961709528660140, 45576855706440520, 229087231033907708, 1139285054092356600, 5611104308926917080, 27390892247090716240, 132623307003710514420, 637333229992836181896, 3041531242991820934488, 14421693905846535650832, 67972746771087135284136, 318584265673384315590608, 1485401635737983585270352, 6891877654051649398771808, 31829958366568330959866722, 146372173012304760045034356, 670368609014709308643509388, 3058448075196556941693359112, 13903120046858488772927497260 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,1

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

Table of n, a(n) for n=4..39.

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

G.f.: x(1-sqrt(1-4x))(17+16x-(10+4x)sqrt(1-4x))/(1-4x)^(11/2). - Sean A. Irvine, Nov 14 2010

MATHEMATICA

CoefficientList[(1/x)(1-Sqrt[1-4x])(17+16x-(10+4x)Sqrt[1-4x])/(1-4x)^(11/2) + O[x]^36, x] (* Jean-Fran├žois Alcover, Feb 08 2016 *)

CROSSREFS

Sequence in context: A159535 A171718 A270409 * A233094 A211421 A097310

Adjacent sequences:  A000470 A000471 A000472 * A000474 A000475 A000476

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 August 18 17:58 EDT 2017. Contains 290732 sequences.