A240881 Chebyshev transform of A107841.

1, 2, 9, 58, 401, 2952, 22759, 181358, 1481751, 12346102, 104505959, 896170608, 7768885801, 67972510202, 599449125609, 5323095489058, 47555513297801, 427127946025752, 3854618439044959, 34934658168463958, 317834095671077751, 2901725605879035502, 26575914921615695759

Offset: 0

Author

Fung Lam, Apr 29 2014

Keywords

• nonn
• easy

Comments

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.

Links

• Fung Lam, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A107841, A160852.

Programs

Mathematica

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 *)

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

Formula

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

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

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

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

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)).