|
|
A215402
|
|
Number of rooted maps of (orientable) genus 4 containing n edges.
|
|
14
|
|
|
225225, 24635754, 1495900107, 66519597474, 2416610807964, 75981252764664, 2141204115631518, 55352670009315660, 1334226671709010578, 30347730709395639732, 657304672067357799042, 13652607304062788395788, 273469313030628783700080, 5306599156694095573465824, 100128328831437989131706976, 1842794650155970906232185656
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
8,1
|
|
LINKS
|
|
|
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, 4];
|
|
PROG
|
(PARI)
A005159_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-12*x))/(6*x);
-y*(y-1)^8*(15812*y^12 - 189744*y^11 + 4708549*y^10 - 24892936*y^9 + 173908449*y^8 - 567987942*y^7 + 1743939189*y^6 - 3485359548*y^5 + 5448471852*y^4 - 6051484928*y^3 + 4633500336*y^2 - 2228416192*y + 517976128)/(81*(y-2)^17*(y+2)^10);
};
|
|
CROSSREFS
|
Rooted maps with n edges of genus g for 0 <= g <= 10: A000168, A006300, A006301, A104742, this sequence, A238355, A238356, A238357, A238358, A238359, A238360.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|