OFFSET
0,5
COMMENTS
1/sqrt((1-x)^2-4rx^4) expands to sum{k=0..floor(n/2), binomial(n-2k,k)binomial(n-3k,k)r^k}.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
a(n)=sum{k=0..floor(n/2), binomial(n-2k, k)binomial(n-3k, k)3^k}.
D-finite with recurrence: n*a(n) = (2*n-1)*a(n-1) - (n-1)*a(n-2) + 12*(n-2)*a(n-4). - Vaclav Kotesovec, Jun 23 2014
a(n) ~ sqrt(3) * (1+sqrt(1+8*sqrt(3)))^n / (sqrt(49+10*sqrt(3)-sqrt(397+884*sqrt(3))) * sqrt(Pi*n) * 2^(n-1)). - Vaclav Kotesovec, Jun 23 2014
MATHEMATICA
CoefficientList[Series[1/Sqrt[(1-x)^2-12*x^4], {x, 0, 20}], x] (* Vaclav Kotesovec, Jun 23 2014 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Sep 10 2004
STATUS
approved