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 A288271 a(n) is the number of rooted maps with n edges and one face on an orientable surface of genus 4. 10
 225225, 12317877, 351683046, 7034538511, 111159740692, 1480593013900, 17302190625720, 182231849209410, 1763184571730010, 15894791312284170, 134951136993773100, 1088243826731751690, 8391311316938069520, 62210659883935683120, 445441857820701181440, 3092035882104030618900 (list; graph; refs; listen; history; text; internal format)
 OFFSET 8,1 LINKS Table of n, a(n) for n=8..23. Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014. FORMULA G.f.: -143*y*(y-1)^8*(1575*y^6 + 13689*y^5 + 4689*y^4 - 34417*y^3 + 11361*y^2 + 7017*y - 2339)/(y-2)^23, 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)((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, 1, 4]; Table[a[n], {n, 8, 23}] (* Jean-François Alcover, Oct 16 2018 *) PROG (PARI) A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x); A288271_ser(N) = { my(y = A000108_ser(N+1)); -143*y*(y-1)^8*(1575*y^6 + 13689*y^5 + 4689*y^4 - 34417*y^3 + 11361*y^2 + 7017*y - 2339)/(y-2)^23; }; Vec(A288271_ser(16)) CROSSREFS Rooted maps of genus 4 with n edges and f faces for 1<=f<=10: this sequence, A288272 f=2, A288273 f=3, A288274 f=4, A288275 f=5, A288276 f=6, A288277 f=7, A288278 f=8, A288279 f=9, A288280 f=10. Column 1 of A269924. Cf. A000108. Sequence in context: A252394 A237848 A269924 * A215402 A204743 A048427 Adjacent sequences: A288268 A288269 A288270 * A288272 A288273 A288274 KEYWORD nonn AUTHOR Gheorghe Coserea, Jun 08 2017 STATUS approved

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Last modified June 2 21:53 EDT 2023. Contains 363100 sequences. (Running on oeis4.)