A348794 a(n) = number of 3-regular one-face rooted maps on orientable surfaces of genus n.

1, 105, 50050, 56581525, 117123756750, 386078943500250, 1857039718236202500, 12277353837189093778125, 106815706684397824557193750, 1183197582943074702620035168750, 16259070931137207808967206912537500, 271431639969559736697533380065719781250

Offset

1,2

Comments

In the paper by Krasko et al. p. 18, Table 2, this sequence is designated "tau^(3)_(+)(g)".

Links

Table of n, a(n) for n=1..12.

Guillaume Chapuy, A new combinatorial identity for unicellular maps, via a direct bijective approach, Advances in Applied Mathematics 47 (2011) 874-893; arXiv preprint, arXiv:1006.5053 [math.CO], 2010.

Evgeniy Krasko, Igor Labutin, and Alexander Omelchenko, Enumeration of 3-regular one-face maps on orientable or non-orientable surface up to all symmetries, arXiv:1901.06591 [math.CO], 2019.

Formula

a(n) = 2*(6*n-3)!/(12^n*n!*(3*n-2)!). - Mireille Bousquet-Mélou, Nov 20 2024

Crossrefs

Cf. A068182, A348795, A348796, A348797.

Sequence in context: A167779 A275461 A054862 * A028917 A145627 A305146

Adjacent sequences: A348791 A348792 A348793 * A348795 A348796 A348797

Keyword

nonn

Author

Michael De Vlieger, Oct 31 2021

Status

approved