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a(n) = number of maximal chord diagrams by genus d^(||)_2n.
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%I #46 Mar 14 2023 09:36:25

%S 1,5,41,509,8229,166377,4016613,113044185,3630535785,131095612845,

%T 5256401729985,231748716159765,11142710564597325,580259659715478225,

%U 32535080119520689725

%N a(n) = number of maximal chord diagrams by genus d^(||)_2n.

%C Also, number of rooted maps with one face, one vertex and n edges on both orientable and non-orientable surfaces.

%H Evgeniy Krasko, <a href="https://arxiv.org/abs/1709.00796">Counting Unlabelled Chord Diagrams of Maximal Genus</a>, arXiv:1709.00796 [math.CO], 2017. See Appendix Table 1.

%H M. Ledoux, <a href="https://doi.org/10.1214/08-AIHP184">A recursion formula for the moments of the Gaussian orthogonal ensemble</a>, Annales de l’Institut Henri Poincaré - Probabilités et Statistiques, 2009, Vol. 45, No. 3, 754-769.

%F Ledoux's article gives a five-term recurrence for related polynomials.

%Y Cf. A291172, A291371, A292111, A035319.

%K nonn,more

%O 1,2

%A _Michael De Vlieger_, Nov 02 2021