A106192 Expansion of sqrt(1-4x)/(1-x^2).

1, -2, -1, -6, -11, -34, -95, -298, -953, -3158, -10677, -36750, -128249, -452774, -1614049, -5801654, -21003739, -76516994, -280293319, -1031794394, -3814819699, -14160035234, -52747353739, -197125162514, -738866581039, -2776933457162, -10462759383943

Offset: 0

Author

Paul Barry, Apr 24 2005

Keywords

• easy
• sign

Comments

Diagonal sums of number triangle A106190.

Crossrefs

Cf. A106190.

Programs

Mathematica

CoefficientList[Series[Sqrt[1-4x]/(1-x^2),{x,0,30}],x] (* Harvey P. Dale, Apr 24 2012 *)

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(2*(n-2*k), n-2*k)/(1-2*(n-2*k)).

D-finite with recurrence: n*a(n) +2*(-2*n+3)*a(n-1) -n*a(n-2) +2*(2*n-3)*a(n-3)=0. - R. J. Mathar, Nov 28 2014