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 A238356 Number of rooted maps of genus 6 containing n edges. 13

%I

%S 24325703325,4416286056750,425671555397220,28948474436455224,

%T 1558252224413413380,70639804918689629112,2802850363447807024080,

%U 99911395098598706576856,3259947795252652107008514,98729808377337068918681196,2805432194025270702468165744

%N Number of rooted maps of genus 6 containing n edges.

%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], (19-March-2014).

%t T[0, 0] = 1; T[n_, g_] /; g < 0 || g > n/2 = 0; T[n_, g_] := T[n, g] = ((4 n - 2)/3 T[n - 1, g] + (2 n - 3) (2 n - 2) (2 n - 1)/12 T[n - 2, g - 1] + 1/2 Sum[(2 k - 1) (2 (n - k) - 1) T[k - 1, i] T[n - k - 1, g - i], {k, 1, n - 1}, {i, 0, g}])/((n + 1)/6);

%t a[n_] := T[n, 6];

%t Table[a[n], {n, 12, 30}] (* _Jean-François Alcover_, Jul 20 2018 *)

%o (PARI) \\ see A238396

%o (PARI)

%o A005159_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-12*x))/(6*x);

%o A238356_ser(N) = {

%o my(y=A005159_ser(N+1));

%o -y*(y-1)^12*(3091382412*y^20 - 61827648240*y^19 + 2494741456179*y^18 - 23821030780564*y^17 + 297709107215018*y^16 - 1898397937026724*y^15 + 11996625283021532*y^14 - 53079600835119544*y^13 + 206468965657569764*y^12 - 637634273350412392*y^11 + 1660605297373850222*y^10 - 3573247507645221112*y^9 + 6390852378647917144*y^8 - 9449999309170921856*y^7 + 11435897504002339264*y^6 - 11175919884930946304*y^5 + 8621441033651120896*y^4 - 5068129528843341824*y^3 + 2141653827725309440*y^2 - 581932716954417152*y + 76958488611567616)/(2187*(y-2)^27*(y+2)^16);

%o };

%o Vec(A238356_ser(11)) \\ _Gheorghe Coserea_, Jun 02 2017

%Y Rooted maps with n edges of genus g for 0 <= g <= 10: A000168, A006300, A006301, A104742, A215402, A238355, this sequence, A238357, A238358, A238359, A238360.

%K nonn

%O 12,1

%A _Joerg Arndt_, Feb 26 2014

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Last modified August 3 20:08 EDT 2020. Contains 336201 sequences. (Running on oeis4.)