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Chebyshev transform of A107841.
1

%I #15 Apr 06 2017 02:28:14

%S 1,2,9,58,401,2952,22759,181358,1481751,12346102,104505959,896170608,

%T 7768885801,67972510202,599449125609,5323095489058,47555513297801,

%U 427127946025752,3854618439044959,34934658168463958,317834095671077751,2901725605879035502,26575914921615695759

%N Chebyshev transform of A107841.

%C This is the Chebyshev transform over the positive strip 0<=x<=1. A160852 may be viewed as the Chebyshev transform over the negative strip -1<=x<=0.

%H Fung Lam, <a href="/A240881/b240881.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: (1+x+x^2 - sqrt(1-10*x+3*x^2-10*x^3+x^4))/(6*x*(1+x^2)).

%F G.f.: F(x/(1+x^2)), where F(x) is the g.f. of A107841.

%F Recurrence: (n+1)*a(n) = (5-n)*a(n-6) + 5*(2*n-7)*a(n-5) + (11-4*n)*a(n-4)

%F + 20*(n-2)*a(n-3) + (5-4*n)*a(n-2) + 5*(2*n-1)*a(n-1), n>=6.

%F a(n) ~ (sqrt(45+20*sqrt(6))/2+sqrt(6)+5/2)^n*sqrt(120-30*sqrt(6)+2*sqrt(30*(6196*sqrt(6)-15159)))/(12*sqrt(Pi*n^3)).

%t CoefficientList[Series[(1+x+x^2 - Sqrt[1-10*x+3*x^2-10*x^3+x^4])/(6*x*(1+x^2)), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Apr 30 2014 *)

%o (PARI) x='x+O('x^50); Vec((1+x+x^2 - sqrt(1-10*x+3*x^2-10*x^3+x^4))/(6*x*(1+x^2))) \\ _G. C. Greubel_, Apr 05 2017

%Y Cf. A107841, A160852.

%K nonn,easy

%O 0,2

%A _Fung Lam_, Apr 29 2014