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

59520825, 8608033980, 672868675017, 37680386599440, 1692352190653740, 64755027944420400, 2190839204960030106, 67194704604610557072, 1901727022434216910002, 50322107898515282999256, 1257582616997225194094310, 29916524874047762719113408, 681758763997451748190036272, 14960113428664295584816860864

Offset: 10

Author

Joerg Arndt, Feb 26 2014

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 10..500
• Sean R. Carrell and Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], (19-March-2014)
• Steven R. Finch, An exceptional convolutional recurrence, arXiv:2408.12440 [math.CO], 22 Aug 2024.

Crossrefs

Row sums of A269925.

Column g=5 of A269919.

Cf. A239918 (unrooted sensed), A348798 (unrooted unsensed)

Rooted maps with n edges of genus g for 0 <= g <= 10: A000168, A006300, A006301, A104742, A215402, this sequence, A238356, A238357, A238358, A238359, A238360.

Programs

Mathematica

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);
a[n_] := T[n, 5];
Table[a[n], {n, 10, 30}] (* Jean-François Alcover, Jul 20 2018 *)

PARI

\\ see A238396

PARI

A005159_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-12*x))/(6*x);
A238355_ser(N) = {
  my(y=A005159_ser(N+1));
  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);
};
Vec(A238355_ser(14)) \\ Gheorghe Coserea, Jun 02 2017