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

0,2

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

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)).

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 *)

Prog

(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

Crossrefs

Cf. A107841, A160852.

Sequence in context: A141787 A377964 A047852 * A224127 A366401 A116867

Adjacent sequences: A240878 A240879 A240880 * A240882 A240883 A240884

Keyword

nonn,easy

Author

Fung Lam, Apr 29 2014

Status

approved