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A288074 a(n) is the number of rooted maps with n edges and 10 faces on an orientable surface of genus 1. 9
6466460, 678405090, 34225196720, 1137369687454, 28442316247080, 576218752277476, 9908748651241088, 149314477245194262, 2017523504473479992, 24868664942648145372, 283389619978690157408, 3017066587822315930220, 30265092793614787511376, 288055728071446557904968, 2616366012933033221518720 (list; graph; refs; listen; history; text; internal format)
OFFSET

11,1

LINKS

Table of n, a(n) for n=11..25.

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, 10, 1];

Table[a[n], {n, 11, 25}] (* 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);

A288074_ser(N) = {

  my(y = A000108_ser(N+1));

  2*y*(y-1)^11*(734641583*y^10 + 3795452665*y^9 - 7483071778*y^8 - 10235465624*y^7 + 25178445968*y^6 - 7563355856*y^5 - 11624244832*y^4 + 8854962048*y^3 - 1433163264*y^2 - 286758144*y + 65790464)/(y-2)^32;

};

Vec(A288074_ser(15))

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, A288073 f=9, this sequence.

Column 10 of A269921.

Sequence in context: A254090 A254097 A209950 * A157787 A115615 A257016

Adjacent sequences:  A288071 A288072 A288073 * A288075 A288076 A288077

KEYWORD

nonn

AUTHOR

Gheorghe Coserea, Jun 05 2017

STATUS

approved

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Last modified August 5 08:27 EDT 2021. Contains 346464 sequences. (Running on oeis4.)