A111964 Expansion of 1/(sqrt(1+4x^2)+x(1-x)).

1, -1, 0, 1, 1, -4, -1, 11, 2, -35, -1, 112, -9, -369, 66, 1237, -327, -4212, 1433, 14527, -5926, -50659, 23749, 178356, -93427, -633225, 363342, 2264885, -1402803, -8154564, 5390861, 29534183, -20655948, -107538835, 79005679, 393462584, -301884895, -1445937945, 1153012596, 5335046209

Offset: 0

Author

Paul Barry, Aug 23 2005

Keywords

• easy
• sign

Comments

Diagonal sums of number triangle A111963.

Programs

Mathematica

CoefficientList[Series[1/(Sqrt[1+4x^2]+x(1-x)),{x,0,40}],x] (* Harvey P. Dale, May 27 2012 *)

Formula

a(n)=sum{k=0..floor(n/2), sum{i=0..floor((n-k)/2), C(2i+2k-n-1, k)C(2i+k-n-1)(-1)^(n-k)*4^i}}