%I M4748 #12 Apr 05 2021 14:01:30
%S 10,240,2246,12656,52164,173776,495820,1256992,2902702,6214208,
%T 12494482,23827440,43430088,76120288,128926232,211867328,338940050,
%U 529346384,809006814,1212404336,1784810764,2584951600,3688170980,5190163680,7211346870,9901950240,13447909290
%N Number of rooted toroidal maps with 3 faces and n vertices and without separating cycles or 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="/A006423/b006423.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 + 1)*(n + 2)*(n + 3)*(29*n^5 + 762*n^4 + 5111*n^3 + 7902*n^2 + 8*n + 5088)/45360. - _Andrew Howroyd_, Apr 04 2021
%o (PARI) a(n) = {n*(n + 1)*(n + 2)*(n + 3)*(29*n^5 + 762*n^4 + 5111*n^3 + 7902*n^2 + 8*n + 5088)/45360}
%Y Column 3 of A343090.
%K nonn
%O 1,1
%A _N. J. A. Sloane_
%E Name clarified and terms a(10) and beyond from _Andrew Howroyd_, Apr 04 2021