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A288281 a(n) is the number of rooted maps with n edges and one face on an orientable surface of genus 5. 10

%I #13 Oct 17 2018 11:29:09

%S 59520825,4304016990,158959754226,4034735959800,79553497760100,

%T 1302772718028600,18475997006212200,233454817237201560,

%U 2682208751185413450,28449551653853229900,281858111998039476900,2632472852850938916000,23350616705746908461520,197910970615681824664800,1610886016462484019585600

%N a(n) is the number of rooted maps with n edges and one face on an orientable surface of genus 5.

%H 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.

%F G.f.: -88179*y*(y-1)^10*(675*y^8 + 9660*y^7 + 19104*y^6 - 38620*y^5 - 26606*y^4 + 51308*y^3 - 10784*y^2 - 5416*y + 1354)/(y-2)^29, where y=A000108(x).

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

%t 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 a[n_] := Q[n, 1, 5];

%t Table[a[n], {n, 10, 24}] (* _Jean-François Alcover_, Oct 17 2018 *)

%Y Rooted maps of genus 5 with n edges and f faces for 1<=f<=10: this sequence, A288282 f=2, A288283 f=3, A288284 f=4, A288285 f=5, A288286 f=6, A288287 f=7, A288288 f=8, A288289 f=9, A288290 f=10.

%Y Column 1 of A269925.

%Y Cf. A000108.

%K nonn

%O 10,1

%A _Gheorghe Coserea_, Jun 09 2017

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)