Let x=- 1, then a (0)-a (1)+a (2)-a (3)+...+a (2n-2)-a (2n-1)+a (2n) = (-)

a( 1)+a(3)+...+a(2n- 1)=( 1/2){[a(0)+a( 1)+...+a(2n)]-[a(0)-a( 1)+a(2)-a(3)+...+a(2n)]}

=( 1/2)[3^(2n)- 1]