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A288083
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a(n) is the number of rooted maps with n edges and 3 faces on an orientable surface of genus 2.
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9
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6468, 258972, 5554188, 85421118, 1059255456, 11270290416, 106853266632, 925572602058, 7454157823560, 56532447160536, 407653880116680, 2815913391715452, 18743188498056288, 120789163612555200, 756589971284883792, 4621041111902656770, 27595482540212519064, 161490751719681569736
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OFFSET
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6,1
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LINKS
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MATHEMATICA
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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, 3, 2];
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PROG
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(PARI)
A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
-6*y*(y-1)^6*(161*y^5 + 4005*y^4 + 4173*y^3 - 10701*y^2 + 2880*y + 560)/(y-2)^17;
};
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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