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A000502 Number of genus 0 rooted maps with 6 faces and n vertices.
(Formerly M5280 N2298)
2
42, 1586, 31388, 442610, 5030004, 49145460, 429166584, 3435601554, 25658464260, 181055975100, 1218601601672, 7880146275092, 49238911113224, 298652277299880, 1764885293279472, 10192638073849554, 57674223198273444, 320430129184331628, 1751190732477786600, 9428906326013866076 (list; graph; refs; listen; history; text; internal format)
OFFSET
5,1
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
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^4*(1-sqrt(1-4*x))*(105+92*x-(84+76*x)*sqrt(1-4*x))/(1-4*x)^7. - Sean A. Irvine, Nov 14 2010
MATHEMATICA
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 *)
PROG
(PARI) seq(n)={my(g=sqrt(1-4*x + O(x*x^n))); Vec((1-g)*(105+92*x - (84+76*x)*g)/((1-4*x)^7))} \\ Andrew Howroyd, Mar 28 2021
CROSSREFS
Column 6 of A269920.
Column 0 of A270410.
Sequence in context: A067638 A155021 A270410 * A215545 A004997 A120815
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, Nov 14 2010
STATUS
approved

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Last modified May 19 12:44 EDT 2024. Contains 372692 sequences. (Running on oeis4.)