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A006430 Number of loopless tree-rooted planar maps with 5 vertices and n faces and no isthmuses.

%I A006430 M4036 #19 Aug 20 2025 11:20:30
%S A006430 0,5,360,7350,73700,474588,2292790,9046807,30676440,92393015,
%T A006430 252872984,639382605,1512137536,3377126024,7176513960,14599539314,
%U A006430 28575632350,54036739617,99069119952,176618150000,306965183268,521265871700,866527603370,1412513294049
%N A006430 Number of loopless tree-rooted planar maps with 5 vertices and n faces and no isthmuses.
%D A006430 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006430 Andrew Howroyd, <a href="/A006430/b006430.txt">Table of n, a(n) for n = 1..1000</a>
%H A006430 T. R. S. Walsh and 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 A006430 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).
%F A006430 a(n) = n*(n + 2)*(n + 3)*(23*n^10 + 963*n^9 + 17544*n^8 + 147952*n^7 + 481675*n^6 - 1052153*n^5 - 7850914*n^4 - 2900162*n^3 + 60869272*n^2 + 37067400*n - 179920800)/(2*11!) for n > 1.
%t A006430 A006430[n_] := If[n == 1, 0, (n*(n + 2)*(n + 3)*(n*(n*(n*(n*(n*(n*(n*(n*(n*(23*n + 963) + 17544) + 147952) + 481675) - 1052153) - 7850914) - 2900162) + 60869272) + 37067400) - 179920800))/79833600];
%t A006430 Array[A006430, 50] (* _Paolo Xausa_, Aug 20 2025 *)
%o A006430 (PARI) a(n)={if(n<2, 0, n*(n + 2)*(n + 3)*(23*n^10 + 963*n^9 + 17544*n^8 + 147952*n^7 + 481675*n^6 - 1052153*n^5 - 7850914*n^4 - 2900162*n^3 + 60869272*n^2 + 37067400*n - 179920800)/(2*11!))} \\ _Andrew Howroyd_, Apr 03 2021
%Y A006430 Column 5 of A342985.
%K A006430 nonn
%O A006430 1,2
%A A006430 _N. J. A. Sloane_
%E A006430 Title improved by _Sean A. Irvine_, Apr 10 2017
%E A006430 Terms a(11) and beyond from _Andrew Howroyd_, Apr 03 2021