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A006418
Number of loopless rooted planar maps with 5 faces and n vertices and no isthmuses.
(Formerly M5268)
2
1, 38, 469, 3008, 12843, 42602, 119042, 293578, 658021, 1367170, 2670203, 4953136, 8794967, 15040494, 24893192, 40031954, 62755945, 96162286, 144361777, 212738384, 308258755, 439838594, 618773310, 859240970, 1178886221, 1599494506, 2147766583, 2856204064
OFFSET
2,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. R. S. Walsh, A. B. Lehman, Counting rooted maps by genus. III: Nonseparable maps, J. Combinatorial Theory Ser. B 18 (1975), 222-259.
Index entries for linear recurrences with constant coefficients, signature (10, -45, 120, -210, 252, -210, 120, -45, 10, -1).
FORMULA
G.f.: x^2 * (14*x^9 -120*x^8 +440*x^7 -879*x^6 +980*x^5 -482*x^4 -92*x^3 +134*x^2 +28*x+1) / (x-1)^10. - Colin Barker, Apr 09 2013
PROG
(PARI) a(n)={if(n<2, 0, (2*n^9 + 81*n^8 + 918*n^7 + 2142*n^6 - 11886*n^5 - 42651*n^4 + 65182*n^3 + 282348*n^2 - 114696*n - 604800)/30240)} \\ Andrew Howroyd, Apr 01 2021
CROSSREFS
Column k=5 of A342980.
Sequence in context: A240258 A254471 A039685 * A160317 A088891 A159784
KEYWORD
nonn
EXTENSIONS
Name clarified and terms a(13) and beyond from Andrew Howroyd, Apr 01 2021
STATUS
approved