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A347951

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

1, 1, 5, 41, 509, 8229, 166377, 4016613, 113044185, 3630535785, 131095612845, 5256401729985, 231748716159765, 11142710564597325, 580259659715478225, 32535080119520689725, 1954232363167878085425, 125190767052413628159825, 8520212311898945786407125

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OFFSET

0,3

COMMENTS

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

LINKS

Table of n, a(n) for n=0..18.

Evgeniy Krasko, Counting Unlabelled Chord Diagrams of Maximal Genus, arXiv:1709.00796 [math.CO], 2017. See Appendix Table 1.

M. Ledoux, A recursion formula for the moments of the Gaussian orthogonal ensemble, Annales de l’Institut Henri Poincaré - Probabilités et Statistiques, 2009, Vol. 45, No. 3, 754-769.

FORMULA

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

MATHEMATICA

a[_?Negative] = 0; a[0|1] = 1;

a[n_] := a[n] = (-(4n-1) a[n-1] + n(2n-3)(10n-9) a[n-2] + 30 Binomial[2n-3, 3] a[n-3] - 240 Binomial[2n-3, 5] a[n-4]) / (n+1);

Array[a, 10] (* Andrei Zabolotskii, Dec 30 2025 *)

CROSSREFS

Cf. A291172, A291371, A292111, A035319.

Sequence in context: A056545 A362111 A325888 * A275787 A009755 A000685

Adjacent sequences: A347948 A347949 A347950 * A347952 A347953 A347954

KEYWORD

nonn