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A238357 Number of genus-7 rooted maps with n edges.

%I A238357 #25 Jan 18 2025 21:58:23
%S A238357 14230536445125,3128879373858000,360626952084151500,
%T A238357 29001816720933903504,1828003659229082834100,96187365300257285300064,
%U A238357 4395215998078319892167640,179153431308203084149883760,6641365771586560905099092466,227189907562197156785567456832,7252879937219595844346639732688
%N A238357 Number of genus-7 rooted maps with n edges.
%H A238357 Andrew Howroyd, <a href="/A238357/b238357.txt">Table of n, a(n) for n = 14..200</a>
%H A238357 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 A238357 Gheorghe Coserea, <a href="/A238357/a238357.txt">The g.f. as a rational function of y=A005159(x)</a>
%H A238357 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 A238357 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 A238357 a[n_] := T[n, 7];
%t A238357 Table[a[n], {n, 14, 30}] (* _Jean-François Alcover_, Jul 20 2018 *)
%o A238357 (PARI) \\ see A238396
%o A238357 (PARI)
%o A238357 system("wget http://oeis.org/A238357/a238357.txt");
%o A238357 A005159_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-12*x))/(6*x);
%o A238357 A238357_ser(N) = subst(read("a238357.txt"), 'y, A005159_ser(N+14));
%o A238357 Vec(A238357_ser(11)) \\ _Gheorghe Coserea_, Jun 03 2017
%Y A238357 Column g=7 of A269919.
%Y A238357 Cf. A239921 (unrooted sensed), A348800 (unrooted unsensed).
%Y A238357 Rooted maps with n edges of genus g for 0 <= g <= 10: A000168, A006300, A006301, A104742, A215402, A238355, A238356, this sequence, A238358, A238359, A238360.
%K A238357 nonn
%O A238357 14,1
%A A238357 _Joerg Arndt_, Feb 26 2014