A288289 a(n) is the number of rooted maps with n edges and 9 faces on an orientable surface of genus 5.

2682208751185413450, 447016944351510642564, 36188783145801243558900, 1924446945220467632598816, 76330117260895762678976496, 2424036981927621898592714592, 64495258714680679471831890624, 1483610943246601143976044602400, 30193909664655985735143003641892, 553279524558089394499396612588296, 9254922250232295721515866705613000, 142890407229849701818261896174135456

Offset: 18

Author

Gheorghe Coserea, Jun 11 2017

Keywords

• nonn

Links

• Gheorghe Coserea, The g.f. as a rational function of y=A000108(x)
• Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014.

Crossrefs

Rooted maps of genus 5 with n edges and f faces for 1<=f<=10: A288281 f=1, A288282 f=2, A288283 f=3, A288284 f=4, A288285 f=5, A288286 f=6, A288287 f=7, A288288 f=8, this sequence, A288290 f=10.

Column 9 of A269925.

Cf. A000108.

Programs

Mathematica

Q[0, 1, 0] = 1; Q[n_, f_, g_] /; n < 0 || f < 0 || g < 0 = 0;
Q[n_, f_, g_] := Q[n, f, g] = 6/(n + 1) ((2n - 1)/3 Q[n - 1, f, g] + (2n - 1)/3 Q[n - 1, f - 1, g] + (2n - 3) (2n - 2) (2n - 1)/12 Q[n - 2, f, g - 1] + 1/2 Sum[l = n - k; Sum[v = f - u; Sum[j = g - i; Boole[l >= 1 && v >= 1 && j >= 0] (2k - 1) (2l - 1) Q[k - 1, u, i] Q[l - 1, v, j], {i, 0, g}], {u, 1, f}], {k, 1, n}]);
a[n_] := Q[n, 9, 5];
Table[a[n], {n, 18, 29}] (* Jean-François Alcover, Oct 17 2018 *)