A243019 Expansion of -(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).

1, 1, 5, 7, 33, 51, 233, 379, 1697, 2851, 12585, 21627, 94449, 165075, 714873, 1266027, 5445441, 9746883, 41687369, 75275227, 320420753, 582881971, 2471008281, 4523575371, 19108837601, 35174066851

Offset

0,3

Links

Table of n, a(n) for n=0..25.

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

Cf. A000108, A128418.

Sequence in context: A104815 A335121 A230997 * A007911 A066172 A175667

Adjacent sequences: A243016 A243017 A243018 * A243020 A243021 A243022

Keyword

nonn

Author

Vladimir Kruchinin, May 29 2014

Status

approved