cp's OEIS Frontend

A288084 a(n) is the number of rooted maps with n edges and 4 faces on an orientable surface of genus 2.

%I A288084 #16 Oct 18 2018 03:03:37
%S A288084 66066,3288327,85421118,1558792200,22555934280,276221817810,
%T A288084 2979641557620,29079129795702,261637840342860,2200626948631386,
%U A288084 17486142956133684,132344695964811720,960323177351524512,6716133365837116980,45466867668336614472,299027167905149145858,1916387674555902480660
%N A288084 a(n) is the number of rooted maps with n edges and 4 faces on an orientable surface of genus 2.
%H A288084 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], 2014.
%t A288084 Q[0, 1, 0] = 1; Q[n_, f_, g_] /; n < 0 || f < 0 || g < 0 = 0;
%t A288084 Q[n_, f_, g_] := Q[n, f, g] = 6/(n + 1) ((2 n - 1)/3 Q[n - 1, f, g] + (2 n - 1)/3 Q[n - 1, f - 1, g] + (2 n - 3) (2 n - 2) (2 n - 1)/12 Q[n - 2, f, g - 1] + 1/2 Sum[l = n - k; Sum[v = f - u; Sum[j = g - i; Boole[l >= 1 && v >= 1 && j >= 0] (2 k - 1) (2 l - 1) Q[k - 1, u, i] Q[l - 1, v, j], {i, 0, g}], {u, 1, f}], {k, 1, n}]);
%t A288084 a[n_] := Q[n, 4, 2];
%t A288084 Table[a[n], {n, 7, 23}] (* _Jean-François Alcover_, Oct 18 2018 *)
%o A288084 (PARI)
%o A288084 A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
%o A288084 A288084_ser(N) = {
%o A288084   my(y = A000108_ser(N+1));
%o A288084   3*y*(y-1)^7*(9318*y^6 + 178328*y^5 + 177929*y^4 - 611583*y^3 + 195218*y^2 + 110388*y - 37576)/(y-2)^20;
%o A288084 };
%o A288084 Vec(A288084_ser(17))
%Y A288084 Rooted maps of genus 2 with n edges and f faces for 1<=f<=10: A006298 f=1, A288082 f=2, A288083 f=3, this sequence, A288085 f=5, A288086 f=6, A288087 f=7, A288088 f=8, A288089 f=9, A288090 f=10.
%Y A288084 Column 4 of A269922, column 2 of A270408.
%Y A288084 Cf. A000108.
%K A288084 nonn
%O A288084 7,1
%A A288084 _Gheorghe Coserea_, Jun 05 2017