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

14230536445125, 3128879373858000, 360626952084151500, 29001816720933903504, 1828003659229082834100, 96187365300257285300064, 4395215998078319892167640, 179153431308203084149883760, 6641365771586560905099092466, 227189907562197156785567456832, 7252879937219595844346639732688

Offset: 14

Author

Joerg Arndt, Feb 26 2014

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 14..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=7 of A269919.

Cf. A239921 (unrooted sensed), A348800 (unrooted unsensed).

Rooted maps with n edges of genus g for 0 <= g <= 10: A000168, A006300, A006301, A104742, A215402, A238355, A238356, this sequence, A238358, 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, 7];
Table[a[n], {n, 14, 30}] (* Jean-François Alcover, Jul 20 2018 *)

PARI

\\ see A238396

PARI

system("wget http://oeis.org/A238357/a238357.txt");
A005159_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-12*x))/(6*x);
A238357_ser(N) = subst(read("a238357.txt"), 'y, A005159_ser(N+14));
Vec(A238357_ser(11)) \\ Gheorghe Coserea, Jun 03 2017