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A238355 Number of rooted maps of genus 5 containing n edges.

%I A238355 #30 Jan 19 2025 00:34:52
%S A238355 59520825,8608033980,672868675017,37680386599440,1692352190653740,
%T A238355 64755027944420400,2190839204960030106,67194704604610557072,
%U A238355 1901727022434216910002,50322107898515282999256,1257582616997225194094310,29916524874047762719113408,681758763997451748190036272,14960113428664295584816860864
%N A238355 Number of rooted maps of genus 5 containing n edges.
%H A238355 Andrew Howroyd, <a href="/A238355/b238355.txt">Table of n, a(n) for n = 10..500</a>
%H A238355 Sean R. Carrell and 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)
%H A238355 Steven R. Finch, <a href="https://arxiv.org/abs/2408.12440">An exceptional convolutional recurrence</a>, arXiv:2408.12440 [math.CO], 22 Aug 2024.
%t A238355 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 A238355 a[n_] := T[n, 5];
%t A238355 Table[a[n], {n, 10, 30}] (* _Jean-François Alcover_, Jul 20 2018 *)
%o A238355 (PARI) \\ see A238396
%o A238355 (PARI)
%o A238355 A005159_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-12*x))/(6*x);
%o A238355 A238355_ser(N) = {
%o A238355   my(y=A005159_ser(N+1));
%o A238355   y*(y-1)^10*(3149956*y^16 - 50399296*y^15 + 1641189689*y^14 - 12178227918*y^13 + 118643174857*y^12 - 572499071300*y^11 + 2690451915197*y^10 - 8657342508522*y^9 + 23652302179098*y^8 - 49891059998872*y^7 + 84432024838000*y^6 - 112355956173344*y^5 + 115338024848256*y^4 - 88846084908160*y^3 + 48488699816960*y^2 - 16837415717888*y + 2841312026112)/(243*(y-2)^22*(y+2)^13);
%o A238355 };
%o A238355 Vec(A238355_ser(14)) \\ _Gheorghe Coserea_, Jun 02 2017
%Y A238355 Row sums of A269925.
%Y A238355 Column g=5 of A269919.
%Y A238355 Cf. A239918 (unrooted sensed), A348798 (unrooted unsensed)
%Y A238355 Rooted maps with n edges of genus g for 0 <= g <= 10: A000168, A006300, A006301, A104742, A215402, this sequence, A238356, A238357, A238358, A238359, A238360.
%K A238355 nonn
%O A238355 10,1
%A A238355 _Joerg Arndt_, Feb 26 2014