A238358 Number of genus-8 rooted maps with n edges.

11288163762500625, 2927974178219879250, 394372363395179602125, 36751560969705187643982, 2663973075006196131775590, 160098273686603663417293308, 8303278159618015743881266599, 381958851175370643701603049354, 15896435050196091382215375181044, 607566907750822335161584110201960

Offset: 16

Author

Joerg Arndt, Feb 26 2014

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 16..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=8 of A269919.

Cf. A239922 (unrooted sensed), A348801 (unrooted unsensed).

Rooted maps with n edges of genus g for 0 <= g <= 10: A000168, A006300, A006301, A104742, A215402, A238355, A238356, A238357, this sequence, A238359, 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, 8];
Table[a[n], {n, 16, 30}] (* Jean-François Alcover, Jul 20 2018 *)

PARI

\\ see A238396