OFFSET
0,3
COMMENTS
1/sqrt(1-2x-(4r-1)x^2+4r^3) expands to give sum{k=0..floor(n/2), binomial(2k,k)binomial(n-k,n-2k)r^k}.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
a(n)=sum{k=0..floor(n/2), binomial(2k, k)binomial(n-k, n-2k)3^k}.
D-finite with recurrence: n*a(n) = (2*n-1)*a(n-1) + 11*(n-1)*a(n-2) - 6*(2*n-3)*a(n-3). - Vaclav Kotesovec, Jun 23 2014
a(n) ~ 2^(2*n+2) / sqrt(21*Pi*n). - Vaclav Kotesovec, Jun 23 2014
MATHEMATICA
CoefficientList[Series[1/Sqrt[1-2*x-11*x^2+12*x^3], {x, 0, 20}], x] (* Vaclav Kotesovec, Jun 23 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul Barry, Sep 10 2004
STATUS
approved