A128058 Expansion of 1/((1-x)sqrt(1-2x+5x^2)).

1, 2, 1, -4, -9, 2, 43, 72, -53, -418, -549, 860, 4161, 4006, -11619, -41104, -24989, 145046, 399571, 89796, -1723259, -3787914, 829841, 19739016, 34642741, -26909998, -219300587, -300591148, 467328447, 2369124842

Offset: 0

Author

Paul Barry, Feb 13 2007

Keywords

• easy
• sign

Comments

Partial sums of A098331. Binomial transform of A128057. Hankel transform is A128056.

Programs

Mathematica

CoefficientList[Series[1/((1-x)Sqrt[1-2x+5x^2]),{x,0,50}],x] (* Harvey P. Dale, Jun 23 2018 *)

Formula

a(n)=sum{k=0..n, sum{j=0..k, C(k,j)*C(k-j,j)*(-1)^j}}

D-finite with recurrence: n*a(n) +(-3*n+1)*a(n-1) +(7*n-6)*a(n-2) +5*(-n+1)*a(n-3)=0. - R. J. Mathar, Jan 23 2020