A238359 Number of genus-9 rooted maps with n edges.

11665426077721040625, 3498878057690404966500, 540996834819906946713375, 57494374008560749302297480, 4724172886681078698955547790, 320061005837218582787265273000, 18618409220753939214291224549409, 956146512935178711199035220384800, 44232688287025023758415781081779828, 1871678026675570344184400604255444240

Offset: 18

Author

Joerg Arndt, Feb 26 2014

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 18..200
• Sean R. Carrell and Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], (19-March-2014).
• Gheorghe Coserea, The g.f. as a rational function of y=A005159(x)
• Steven R. Finch, An exceptional convolutional recurrence, arXiv:2408.12440 [math.CO], 22 Aug 2024.

Crossrefs

Column g=9 of A269919.

Rooted maps with n edges of genus g for 0 <= g <= 10: A000168, A006300, A006301, A104742, A215402, A238355, A238356, A238357, A238358, this sequence, A238360.

Programs

Mathematica

T[0, 0] = 1; T[n_, g_] /; g < 0 || g > n/2 = 0; T[n_, g_] := T[n, g] = ((4 n - 2)/3 T[n - 1, g] + (2 n - 3) (2 n - 2) (2 n - 1)/12 T[n - 2, g - 1] + 1/2 Sum[(2 k - 1) (2 (n - k) - 1) T[k - 1, i] T[n - k - 1, g - i], {k, 1, n - 1}, {i, 0, g}])/((n + 1)/6);
a[n_] := T[n, 9];
Table[a[n], {n, 18, 30}] (* Jean-François Alcover, Jul 20 2018 *)

PARI

\\ see A238396