A270822 Expansion of 1/((1-4*x^2)^(3/2)-2*x*(1-4*x^2)).

1, 2, 10, 24, 86, 224, 708, 1920, 5734, 15872, 46124, 129024, 369916, 1040384, 2962760, 8355840, 23714950, 66977792, 189768220, 536346624, 1518330516, 4292870144, 12147349560, 34351349760, 97181500636, 274844352512, 777462405688

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Formula

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

a(n) ~ 2^((3*n+1)/2). - Vaclav Kotesovec, Mar 23 2016

Mathematica

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 *)

Prog

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

Crossrefs

Cf. A000984.

Sequence in context: A233266 A222848 A119062 * A248117 A345695 A336958

Adjacent sequences: A270819 A270820 A270821 * A270823 A270824 A270825

Keyword

nonn

Author

Vladimir Kruchinin, Mar 23 2016

Status

approved