OFFSET
0,3
FORMULA
G.f.: (x/((1-x))+1/((-sqrt(5*x^2-2*x+1)+x+1))*x*(1-(5*x-1)/(sqrt(5*x^2-2*x+1)))). - Vladimir Kruchinin, Oct 04 2015
a(n) = Sum_{j=0..n/2}((-1)^j*binomial(n,j)*binomial(n-j-1,n-2*j)). - Vladimir Kruchinin, Oct 04 2015
MATHEMATICA
CoefficientList[Series[(x/((1 - x)) + 1/((-Sqrt[5 x^2 - 2 x + 1] + x + 1)) x (1 - (5 x - 1)/(Sqrt[5 x^2 - 2 x + 1]))), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 05 2015 *)
PROG
(PARI) a(n)=sum(k=0, n, polcoeff((1+x-x^2)^n, n+k))
(Maxima)
a(n):=sum((-1)^j*binomial(n, j)*binomial(n-j-1, n-2*j), j, 0, n/2); /* Vladimir Kruchinin, Oct 04 2015 */
(PARI) a(n) = sum(k=0, n/2, (-1)^k*binomial(n, k)*binomial(n-k-1, n-2*k));
vector(40, n, a(n-1)) \\ Altug Alkan, Oct 04 2015
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Mar 11 2005
STATUS
approved