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Number of loopless rooted planar maps with 5 faces and n vertices and no isthmuses.
(Formerly M5268)
2

%I M5268 #22 Jul 19 2024 08:43:18

%S 1,38,469,3008,12843,42602,119042,293578,658021,1367170,2670203,

%T 4953136,8794967,15040494,24893192,40031954,62755945,96162286,

%U 144361777,212738384,308258755,439838594,618773310,859240970,1178886221,1599494506,2147766583,2856204064

%N Number of loopless rooted planar maps with 5 faces and n vertices and no isthmuses.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Andrew Howroyd, <a href="/A006418/b006418.txt">Table of n, a(n) for n = 2..1000</a>

%H T. R. S. Walsh, A. B. Lehman, <a href="http://dx.doi.org/10.1016/0095-8956(75)90050-7">Counting rooted maps by genus. III: Nonseparable maps</a>, J. Combinatorial Theory Ser. B 18 (1975), 222-259.

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10, -45, 120, -210, 252, -210, 120, -45, 10, -1).

%F 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

%o (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

%Y Column k=5 of A342980.

%K nonn

%O 2,2

%A _N. J. A. Sloane_

%E Name clarified and terms a(13) and beyond from _Andrew Howroyd_, Apr 01 2021