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

%I A238358 #24 Jan 18 2025 21:58:28
%S A238358 11288163762500625,2927974178219879250,394372363395179602125,
%T A238358 36751560969705187643982,2663973075006196131775590,
%U A238358 160098273686603663417293308,8303278159618015743881266599,381958851175370643701603049354,15896435050196091382215375181044,607566907750822335161584110201960
%N A238358 Number of genus-8 rooted maps with n edges.
%H A238358 Andrew Howroyd, <a href="/A238358/b238358.txt">Table of n, a(n) for n = 16..200</a>
%H A238358 Sean R. Carrell and 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 A238358 Gheorghe Coserea, <a href="/A238358/a238358.txt">The g.f. as a rational function of y=A005159(x)</a>
%H A238358 Steven R. Finch, <a href="https://arxiv.org/abs/2408.12440">An exceptional convolutional recurrence</a>, arXiv:2408.12440 [math.CO], 22 Aug 2024.
%t A238358 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 A238358 a[n_] := T[n, 8];
%t A238358 Table[a[n], {n, 16, 30}] (* _Jean-François Alcover_, Jul 20 2018 *)
%o A238358 (PARI) \\ see A238396
%Y A238358 Column g=8 of A269919.
%Y A238358 Cf. A239922 (unrooted sensed), A348801 (unrooted unsensed).
%Y A238358 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 A238358 nonn
%O A238358 16,1
%A A238358 _Joerg Arndt_, Feb 26 2014