OFFSET
3,1
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
T. R. S. Walsh, Combinatorial Enumeration of Non-Planar Maps. Ph.D. Dissertation, Univ. of Toronto, 1971.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 3..1000
W. T. Tutte, On the enumeration of planar maps, Bull. Amer. Math. Soc. 74 1968 64-74.
T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus, J. Comb. Thy B13 (1972), 122-141 and 192-218.
FORMULA
G.f.: x*(1-sqrt(1-4*x))*(11+12*x+9*sqrt(1-4*x))/(4*(4*x-1)^4). - Sean A. Irvine, Nov 14 2010
MATHEMATICA
Rest[CoefficientList[Series[(1 - Sqrt[1 - 4 x]) (11 + 12 x + 9 Sqrt[1 - 4 x]) / (4 (4 x - 1)^4), {x, 0, 40}], x]] (* Vincenzo Librandi, Jun 06 2017 *)
PROG
(PARI)
A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
A006295_ser(N) = {
my(y = A000108_ser(N+1)); y*(y-1)^3*(y^2 + 15*y - 6)/(y-2)^8;
};
Vec(A006295_ser(31)) \\ Gheorghe Coserea, Jun 04 2017
(PARI) my(x = 'x + O('x^60)); Vec(x*(1-sqrt(1-4*x))*(11+12*x+9*sqrt(1-4*x))/(4*(4*x-1)^4)) \\ Michel Marcus, Jun 05 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, Nov 14 2010
STATUS
approved