%I M5102 #17 Apr 05 2021 18:50:28

%S 20,651,8344,64667,361884,1607125,5997992,19535997,57014776,151986562,

%T 375470160,869285378,1902886024,3966657702,7920130544,15220758070,

%U 28268206764,50910912965,89176474920,152305796565,254193384900,415363487955,665644575960,1047743815755

%N Number of nonseparable rooted toroidal maps with n + 5 edges and n + 1 vertices.

%C The number of faces is 4. - _Andrew Howroyd_, Apr 05 2021

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

%H Andrew Howroyd, <a href="/A006410/b006410.txt">Table of n, a(n) for n = 2..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) = 20 * binomial(n + 6, 8) + 471 * binomial(n + 6, 9) + 2734 * binomial(n + 6, 10) + 5388 * binomial(n + 6, 11) + 3264 * binomial(n + 6, 12) [From Walsh]. - _Sean A. Irvine_, Apr 03 2017

%F a(n) = binomial(n + 6, 8)*(136*n^4 + 790*n^3 + 447*n^2 - 180*n - 24)/495. - _Andrew Howroyd_, Apr 05 2021

%o (PARI) a(n) = {binomial(n + 6, 8)*(136*n^4 + 790*n^3 + 447*n^2 - 180*n - 24)/495} \\ _Andrew Howroyd_, Apr 05 2021

%Y Column 4 of A342989.

%K nonn

%O 2,1

%A _N. J. A. Sloane_

%E Terms a(9) and beyond from _Andrew Howroyd_, Apr 05 2021