%I M5104 #11 Apr 05 2021 14:00:38
%S 20,831,12656,109075,648792,2978245,11293436,36973989,107727724,
%T 285451894,699013380,1601397330,3465135024,7135903782,14072047976,
%U 26707904230,48991682628,87164772761,150869282184,254695011933,420306632200,679327313795,1077197343300,1678276223715
%N Number of rooted toroidal maps with 4 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="/A006424/b006424.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)*(n + 4)*(136*n^7 + 6554*n^6 + 98165*n^5 + 516860*n^4 + 763064*n^3 + 306776*n^2 + 2220955*n - 586110)/19958400. - _Andrew Howroyd_, Apr 04 2021
%o (PARI) a(n) = {n*(n + 1)*(n + 2)*(n + 3)*(n + 4)*(136*n^7 + 6554*n^6 + 98165*n^5 + 516860*n^4 + 763064*n^3 + 306776*n^2 + 2220955*n - 586110)/19958400} \\ _Andrew Howroyd_, Apr 04 2021
%Y Column 4 of A343090.
%K nonn
%O 1,1
%A _N. J. A. Sloane_
%E Name clarified and terms a(9) and beyond from _Andrew Howroyd_, Apr 04 2021