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Number of genus-8 rooted maps with n edges.
14

%I #17 Aug 23 2024 03:18:58

%S 11288163762500625,2927974178219879250,394372363395179602125,

%T 36751560969705187643982,2663973075006196131775590,

%U 160098273686603663417293308,8303278159618015743881266599,381958851175370643701603049354,15896435050196091382215375181044,607566907750822335161584110201960

%N Number of genus-8 rooted maps with n edges.

%H Sean R. Carrell, Guillaume Chapuy, <a href="http://arxiv.org/abs/1402.6300">Simple recurrence formulas to count maps on orientable surfaces</a>, arXiv:1402.6300 [math.CO], (19-March-2014)

%H Gheorghe Coserea, <a href="/A238358/a238358.txt">The g.f. as a rational function of y=A005159(x)</a>

%H S. R. Finch, <a href="https://arxiv.org/abs/2408.12440">An exceptional convolutional recurrence</a>, arXiv:2408.12440 [math.CO], 22 Aug 2024.

%t 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);

%t a[n_] := T[n, 8];

%t Table[a[n], {n, 16, 30}] (* _Jean-François Alcover_, Jul 20 2018 *)

%o (PARI) \\ see A238396

%Y Rooted maps with n edges of genus g for 0 <= g <= 10: A000168, A006300, A006301, A104742, A215402, A238355, A238356, A238357, this sequence, A238359, A238360.

%K nonn

%O 16,1

%A _Joerg Arndt_, Feb 26 2014