|
%I #13 Jul 20 2018 03:18:10
%S 15230046989184655753125,5199629454143883380553750,
%T 909887917857275652461097750,108861830345440643086946970900,
%U 10021124647635764856828690342402,757187906770815991999545249667404,48918614114003431712044170834572688,2779227352989564224315657269511192976,141720718575991991799057452443438430580
%N Number of genus-10 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="/A238360/a238360.txt">The g.f. as a rational function of y=A005159(x)</a>
%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, 10];
%t Table[a[n], {n, 20, 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, A238358, A238359, this sequence.
%K nonn
%O 20,1
%A _Joerg Arndt_, Feb 26 2014
|
