A141344 Expansion of (2-sqrt(1+4x))/(2-x-sqrt(1+4x)).

1, 1, 3, 7, 19, 45, 123, 285, 807, 1771, 5407, 10587, 37627, 57619, 279783, 231615, 2307339, -387531, 21769251, -28249347, 235837791, -539858235, 2857845723, -8509970007, 37342507167, -126289733319, 510715973643, -1837291760147

Offset: 0

Author

Paul Barry, Jun 26 2008

Keywords

• easy
• sign

Comments

Row sums of A141343. Hankel transform is 2^n.

Image of A052961 under the Riordan array (c(-x),xc(-x)^2), c(x) the g.f. of A000108. [From Paul Barry, Jan 29 2009]

Programs

Mathematica

CoefficientList[Series[(2-Sqrt[1+4x])/(2-x-Sqrt[1+4x]),{x,0,30}],x] (* Harvey P. Dale, Jan 14 2013 *)

Formula

Conjectured to be D-finite with recurrence: 3*(n-1)*a(n) +2*(2*n-11)*a(n-1) +(79-31*n)*a(n-2) +2*(2*n-5)*a(n-3)=0. - R. J. Mathar, Oct 25 2012