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A000502
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Number of genus 0 rooted maps with 6 faces with n vertices.
(Formerly M5280 N2298)
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1
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42, 1586, 31388, 442610, 5030004, 49145460, 429166584, 3435601554, 25658464260, 181055975100, 1218601601672, 7880146275092, 49238911113224, 298652277299880, 1764885293279472, 10192638073849554, 57674223198273444, 320430129184331628, 1751190732477786600, 9428906326013866076, 50084560529695713560, 262767521450593566680, 1363049865350949194640, 6997091408385651436500, 35574379172542272659688, 179258908485659235515352, 895827468451622607205200, 4442385594472223942397672, 21871555968464155937448080, 106958771000949466098945104, 519767712768164680745022944, 2510872436703684655047207762, 12061854932881499884016376036, 57638984943605113572323531340, 274068077621341051602455876520
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OFFSET
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5,1
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REFERENCES
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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.
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LINKS
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Table of n, a(n) for n=5..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.
Notes
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FORMULA
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G.f.: x(1-sqrt(1-4x))(105+92x-(84 + 76x)sqrt(1-4x))/(1-4x)^7. - Sean A. Irvine, Nov 14 2010
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MATHEMATICA
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CoefficientList[ x(1-Sqrt[1-4x])(105+92x-(84+76x)Sqrt[1-4x])/(1-4x)^7/x^2 + O[x]^30, x] (* Jean-François Alcover, Feb 09 2016 *)
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CROSSREFS
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Sequence in context: A067638 A155021 A270410 * A215545 A004997 A120815
Adjacent sequences: A000499 A000500 A000501 * A000503 A000504 A000505
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Sean A. Irvine, Nov 14 2010
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STATUS
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approved
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