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A288288 a(n) is the number of rooted maps with n edges and 8 faces on an orientable surface of genus 5. 11
233454817237201560, 35801820369640556595, 2677324515710001081372, 131989618396827099239715, 4869474711666664850333856, 144282707675416905279319800, 3591928999997575304490876960, 77515666515764938993111323048, 1483610943246601143976044602400, 25624962301264473700614835484334, 404881818003827869935873694190904, 5916336815178383154031082792690874 (list; graph; refs; listen; history; text; internal format)
OFFSET

17,1

LINKS

Table of n, a(n) for n=17..28.

Gheorghe Coserea, The g.f. as a rational function of y=A000108(x)

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) ((2n - 1)/3 Q[n - 1, f, g] + (2n - 1)/3 Q[n - 1, f - 1, g] + (2n - 3) (2n - 2) (2n - 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] (2k - 1) (2l - 1) Q[k - 1, u, i] Q[l - 1, v, j], {i, 0, g}], {u, 1, f}], {k, 1, n}]);

a[n_] := Q[n, 8, 5];

Table[a[n], {n, 17, 28}] (* Jean-Fran├žois Alcover, Oct 17 2018 *)

CROSSREFS

Rooted maps of genus 5 with n edges and f faces for 1<=f<=10: A288281 f=1, A288282 f=2, A288283 f=3, A288284 f=4, A288285 f=5, A288286 f=6, A288287 f=7, this sequence, A288289 f=9, A288290 f=10.

Column 8 of A269925.

Cf. A000108.

Sequence in context: A094676 A327760 A054213 * A080128 A132901 A058292

Adjacent sequences:  A288285 A288286 A288287 * A288289 A288290 A288291

KEYWORD

nonn

AUTHOR

Gheorghe Coserea, Jun 11 2017

STATUS

approved

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Last modified December 13 17:17 EST 2019. Contains 329970 sequences. (Running on oeis4.)