OFFSET
0,1
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Robert Israel, Table of n, a(n) for n = 0..1000
M. F. Sykes and M. E. Fisher, Antiferromagnetic susceptibility of the plane square and honeycomb Ising lattices, Physica, 28 (1962), 919-938.
FORMULA
G.f.: (1+x)/(1-x) + ((1-6*x+x^2)/(1-x^2))*Sum_{k>=0} (2*k)!^2 * (x*(1-x)^2/(1+x)^4)^k/k!^4. - Robert Israel, Nov 27 2017
a(n) ~ -2 * (1 + sqrt(2))^(2*n) / (Pi*n^2). - Vaclav Kotesovec, Nov 28 2017
MAPLE
u:=v->((1+v^2)*(1-(2/Pi)*(1-6*v^2+v^4)*EllipticK(4*v*(1-v^2)/(1+v^2)^2)/(1+v^2)^2)/2*v):
S:= series(u((1-v)/(1+v))/((1-v)/(1+v))^2, v, 101):
seq(coeff(S, v, j), j=0..100, 2); # Sean A. Irvine, Nov 27 2017
MATHEMATICA
Table[SeriesCoefficient[(1 + v)/(1 - v)^3 ((1 - v)^2 + 2/Pi (1 - 6 v + v^2) EllipticK[(16 v^2)/(1 - v)^4]), {v, 0, k}], {k, 0, 100}] (* Jan Mangaldan, Nov 28 2020 *)
CROSSREFS
KEYWORD
sign
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, Nov 27 2017
STATUS
approved