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 A269925 Triangle read by rows: T(n,f) is the number of rooted maps with n edges and f faces on an orientable surface of genus 5. 13
 59520825, 4304016990, 4304016990, 158959754226, 354949166565, 158959754226, 4034735959800, 14805457339920, 14805457339920, 4034735959800, 79553497760100, 420797306522502, 691650582088536, 420797306522502, 79553497760100, 1302772718028600, 9220982517965400, 21853758736216200, 21853758736216200, 9220982517965400, 1302772718028600 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 10,1 COMMENTS Row n contains n-9 terms. LINKS Gheorghe Coserea, Rows n = 10..210, flattened Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014. EXAMPLE Triangle starts: n\f  [1]             [2]             [3]             [4] [10] 59520825; [11] 4304016990,     4304016990; [12] 15895975422,    354949166565,   158959754226; [13] 4034735959800,  14805457339920, 14805457339920, 4034735959800; [14] ... 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}]); Table[Q[n, f, 5], {n, 10, 15}, {f, 1, n-9}] // Flatten (* Jean-François Alcover, Aug 10 2018 *) PROG (PARI) N = 15; G = 5; gmax(n) = min(n\2, G); Q = matrix(N + 1, N + 1); Qget(n, g) = { if (g < 0 || g > n/2, 0, Q[n+1, g+1]) }; Qset(n, g, v) = { Q[n+1, g+1] = v }; Quadric({x=1}) = {   Qset(0, 0, x);   for (n = 1, length(Q)-1, for (g = 0, gmax(n),     my(t1 = (1+x)*(2*n-1)/3 * Qget(n-1, g),        t2 = (2*n-3)*(2*n-2)*(2*n-1)/12 * Qget(n-2, g-1),        t3 = 1/2 * sum(k = 1, n-1, sum(i = 0, g,        (2*k-1) * (2*(n-k)-1) * Qget(k-1, i) * Qget(n-k-1, g-i))));     Qset(n, g, (t1 + t2 + t3) * 6/(n+1)))); }; Quadric('x); concat(apply(p->Vecrev(p/'x), vector(N+1 - 2*G, n, Qget(n-1 + 2*G, G)))) 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, A288288 f=8, A288289 f=9, A288290 f=10. Row sums give A238355 (column 5 of A269919). Cf. A035309, A269921, A269922, A269923, A269924, A270406, A270407, A270408, A270409, A270410, A270411, A270412. Sequence in context: A320211 A320220 A034644 * A288281 A238355 A104329 Adjacent sequences:  A269922 A269923 A269924 * A269926 A269927 A269928 KEYWORD nonn,tabl AUTHOR Gheorghe Coserea, Mar 15 2016 STATUS approved

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Last modified January 23 16:47 EST 2020. Contains 331172 sequences. (Running on oeis4.)