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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
59520825, 4304016990, 158959754226, 4034735959800, 79553497760100, 1302772718028600, 18475997006212200, 233454817237201560, 2682208751185413450, 28449551653853229900, 281858111998039476900, 2632472852850938916000, 23350616705746908461520, 197910970615681824664800, 1610886016462484019585600
OFFSET
10,1
LINKS
Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014.
FORMULA
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).
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, 1, 5];
Table[a[n], {n, 10, 24}] (* Jean-François Alcover, Oct 17 2018 *)
CROSSREFS
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.
Column 1 of A269925.
Cf. A000108.
Sequence in context: A320220 A034644 A269925 * A238355 A104329 A104333
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Jun 09 2017
STATUS
approved