A270822 - OEIS

%I #13 Mar 25 2016 07:16:59

%S 1,2,10,24,86,224,708,1920,5734,15872,46124,129024,369916,1040384,

%T 2962760,8355840,23714950,66977792,189768220,536346624,1518330516,

%U 4292870144,12147349560,34351349760,97181500636,274844352512,777462405688

%N Expansion of 1/((1-4*x^2)^(3/2)-2*x*(1-4*x^2)).

%F a(n) = (n+1)*2^n*Sum_{i=0..n/2}(binomial((n-1)/2,i)/(n-2*i+1)).

%F a(n) ~ 2^((3*n+1)/2). - _Vaclav Kotesovec_, Mar 23 2016

%t CoefficientList[Series[1/((1 - 4 x^2)^(3/2) - 2 x (1 - 4 x^2)), {x, 0, 26}], x] (* _Michael De Vlieger_, Mar 23 2016 *)

%o (Maxima)

%o a(n):=(n+1)*2^(n)*sum(binomial((n-1)/2,i)/(n-2*i+1),i,0,n/2);

%o (PARI) x='x+O('x^200); Vec(1/((1-4*x^2)^(3/2)-2*x*(1-4*x^2))) \\ _Altug Alkan_, Mar 23 2016

%Y Cf. A000984.

%K nonn

%O 0,2

%A _Vladimir Kruchinin_, Mar 23 2016