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Number of rooted 4-regular one-face maps on genus g surface.
1

%I #16 Sep 04 2017 04:23:23

%S 1,45,9450,4729725,4341887550,6352181485650,13566444744352500,

%T 39834473380605028125,153946961458244898693750,

%U 757572997336023146471943750,4625189759553876588251163487500,34307345041490879593353005168531250,303883906271359598859584503473567187500,3168250194798584983481619521143486701562500,38405528861348447169764191835301345796340625000

%N Number of rooted 4-regular one-face maps on genus g surface.

%H Evgeniy Krasko, Alexander Omelchenko, <a href="https://doi.org/10.1016/j.ejc.2016.12.004">Enumeration of 4-regular one-face maps</a>, European Journal of Combinatorics, Volume 62, 2017, Pages 167-177.

%F a(g) = 2*((4g-2)!)/((4^g)*(g!)*((g-1)!)).

%e On a torus (g=1) there exists only one 4-regular one-face map.

%K nonn

%O 1,2

%A _Evgeniy Krasko_, Sep 03 2017