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%I #23 Nov 21 2024 07:54:52
%S 1,105,50050,56581525,117123756750,386078943500250,
%T 1857039718236202500,12277353837189093778125,
%U 106815706684397824557193750,1183197582943074702620035168750,16259070931137207808967206912537500,271431639969559736697533380065719781250
%N a(n) = number of 3-regular one-face rooted maps on orientable surfaces of genus n.
%C In the paper by Krasko et al. p. 18, Table 2, this sequence is designated "tau^(3)_(+)(g)".
%H Guillaume Chapuy, <a href="https://doi.org/10.1016/j.aam.2011.04.004">A new combinatorial identity for unicellular maps, via a direct bijective approach</a>, Advances in Applied Mathematics 47 (2011) 874-893; <a href="https://arxiv.org/abs/1006.5053">arXiv preprint</a>, arXiv:1006.5053 [math.CO], 2010.
%H Evgeniy Krasko, Igor Labutin, and Alexander Omelchenko, <a href="https://arxiv.org/abs/1901.06591">Enumeration of 3-regular one-face maps on orientable or non-orientable surface up to all symmetries</a>, arXiv:1901.06591 [math.CO], 2019.
%F a(n) = 2*(6*n-3)!/(12^n*n!*(3*n-2)!). - _Mireille Bousquet-Mélou_, Nov 20 2024
%Y Cf. A068182, A348795, A348796, A348797.
%K nonn
%O 1,2
%A _Michael De Vlieger_, Oct 31 2021