login
Number of loopless tree-rooted planar maps with 5 vertices and n faces and no isthmuses.
(Formerly M4036)
2

%I M4036 #15 Apr 04 2021 13:39:28

%S 0,5,360,7350,73700,474588,2292790,9046807,30676440,92393015,

%T 252872984,639382605,1512137536,3377126024,7176513960,14599539314,

%U 28575632350,54036739617,99069119952,176618150000,306965183268,521265871700,866527603370,1412513294049

%N Number of loopless tree-rooted planar maps with 5 vertices and n faces 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="/A006430/b006430.txt">Table of n, a(n) for n = 1..1000</a>

%H 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.

%F 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.

%o (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 Column 5 of A342985.

%K nonn

%O 1,2

%A _N. J. A. Sloane_

%E Title improved by _Sean A. Irvine_, Apr 10 2017

%E Terms a(11) and beyond from _Andrew Howroyd_, Apr 03 2021