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A111966 Expansion of 1/(sqrt(1-6x+5x^2)-x). 4

%I

%S 1,4,18,86,424,2128,10798,55190,283510,1461730,7557166,39153338,

%T 203188892,1055863564,5492668906,28598497610,149012237696,

%U 776904940576,4052654604042,21149661562298,110415949871240,576636302495488

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

%C Row sums of number triangle A111965.

%H Vincenzo Librandi, <a href="/A111966/b111966.txt">Table of n, a(n) for n = 0..300</a>

%F 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).

%F 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

%F a(n) ~ (sqrt(5)+3)^n/sqrt(5). - _Vaclav Kotesovec_, Oct 24 2012

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

%K easy,nonn

%O 0,2

%A _Paul Barry_, Aug 23 2005

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Last modified July 5 21:00 EDT 2020. Contains 335473 sequences. (Running on oeis4.)