A111966 Expansion of 1/(sqrt(1-6x+5x^2)-x).

1, 4, 18, 86, 424, 2128, 10798, 55190, 283510, 1461730, 7557166, 39153338, 203188892, 1055863564, 5492668906, 28598497610, 149012237696, 776904940576, 4052654604042, 21149661562298, 110415949871240, 576636302495488

Offset: 0

Author

Paul Barry, Aug 23 2005

Keywords

• easy
• nonn

Comments

Row sums of number triangle A111965.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300

Programs

Mathematica

CoefficientList[Series[1/(Sqrt[1-6*x+5*x^2]-x), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 24 2012 *)

Formula

a(n) = Sum_{k=0..n} Sum_{j=0..n} C((k+2j-1)/2,j)*C(j,n-j-k)*(-6)^(k-n+2*j) * 5^(n-k-j).

D-finite with recurrence: n*a(n) = 3*(4*n-3)*a(n-1) - 3*(15*n-23)*a(n-2) + 18*(3*n-7) * a(n-3) - 20*(n-3)*a(n-4). - Vaclav Kotesovec, Oct 24 2012

a(n) ~ (sqrt(5)+3)^n/sqrt(5). - Vaclav Kotesovec, Oct 24 2012