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A288073 a(n) is the number of rooted maps with n edges and 9 faces on an orientable surface of genus 1. 9
1385670, 126264820, 5593305476, 164767964504, 3682811916980, 67173739068760, 1046677747672360, 14373136466094880, 177882700353757460, 2017523504473479992, 21241931655650633720, 209732362862241103248, 1957830216739337392584, 17394726697224718134384, 147908195064869691109072 (list; graph; refs; listen; history; text; internal format)
OFFSET

10,1

LINKS

Table of n, a(n) for n=10..24.

Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014.

MATHEMATICA

Q[0, 1, 0] = 1; Q[n_, f_, g_] /; n < 0 || f < 0 || g < 0 = 0;

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}]);

a[n_] := Q[n, 9, 1];

Table[a[n], {n, 10, 24}] (* Jean-Fran├žois Alcover, Oct 18 2018 *)

PROG

(PARI)

A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);

A288073_ser(N) = {

  my(y = A000108_ser(N+1));

  -2*y*(y-1)^10*(58911256*y^9 + 315266323*y^8 - 563073084*y^7 - 706445836*y^6 + 1588166368*y^5 - 488205920*y^4 - 472512192*y^3 + 315108288*y^2 - 44342784*y - 2179584)/(y-2)^29;

};

Vec(A288073_ser(17))

CROSSREFS

Rooted maps of genus 1 with n edges and f faces for 1<=f<=10: A002802(with offset 2) f=1, A006295 f=2, A006296 f=3, A288071 f=4, A288072 f=5, A287046 f=6, A287047 f=7, A287048 f=8, this sequence, A288074 f=10.

Column 9 of A269921.

Sequence in context: A229420 A249882 A252446 * A237240 A052242 A234548

Adjacent sequences:  A288070 A288071 A288072 * A288074 A288075 A288076

KEYWORD

nonn

AUTHOR

Gheorghe Coserea, Jun 05 2017

STATUS

approved

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Last modified February 20 07:54 EST 2020. Contains 332069 sequences. (Running on oeis4.)