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A288089
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a(n) is the number of rooted maps with n edges and 9 faces on an orientable surface of genus 2.
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9
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1293938646, 140725699686, 7454157823560, 261637840342860, 6928413234959820, 148755268498286436, 2710382626755160416, 43241609165618454096, 617910462111714896820, 8044640800289827566756, 96690983139765469347024, 1084226645505246141589704, 11439196912435362172792536, 114351801899024314438876200
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OFFSET
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12,1
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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, 9, 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)^12*(12205186004*y^11 + 144345246789*y^10 + 83883548039*y^9 - 978172313331*y^8 + 436600889944*y^7 + 1435650005364*y^6 - 1511798886368*y^5 + 121539026592*y^4 + 411304907520*y^3 - 171035694144*y^2 + 14120686592*y + 1573053440)/(y-2)^35;
};
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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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