OFFSET
0,3
FORMULA
a(n) = sum(i=0..floor(n/2), 2^i*binomial(n,i)).
G.f. A(x) = (x*C'(2*x^2))/(C(2*x^2)*(1-x*C(2*x^2))), where C(x) is g.f. of A000108.
a(n) ~ 2^(3*n/2) * (2+sqrt(2) + (-1)^n*(2-sqrt(2))) / sqrt(2*Pi*n). - Vaclav Kotesovec, May 29 2014
D-finite with recurrence: n^2*a(n) = (3*n^2-4)*a(n-1) + 4*(2*n^2 - 2*n - 1)*a(n-2) - 24*(n-2)*(n+1)*a(n-3). - Vaclav Kotesovec, May 29 2014
MATHEMATICA
CoefficientList[Series[-(2*x*Sqrt[1-8*x^2]-2*x)/(16*x^3+Sqrt[1-8*x^2]*(4*x^2+2*x-1)-8*x^2-2*x+1), {x, 0, 20}], x] (* Vaclav Kotesovec, May 29 2014 *)
PROG
(Maxima)
a(n):=sum(2^(i)*binomial(n, i), i, 0, floor((n)/2));
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, May 29 2014
STATUS
approved