A160852 Chebyshev transform of A107841.

1, 2, 11, 66, 461, 3448, 27061, 219702, 1829851, 15547142, 134224361, 1174119120, 10383783641, 92691197962, 834047700091, 7557110252538, 68890745834341, 631392034936040, 5814520777199261, 53776065007163886, 499275423496447211

Offset: 0

Author

Paul Barry, May 28 2009

Keywords

• easy
• nonn

Links

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

Programs

Magma

m:=25; R:=PowerSeriesRing(Rationals(), m); Coefficients(R!((1+x-x^2-Sqrt(1-10*x-x^2+10*x^3+x^4))/(6*x*(1-x^2)))) // G. C. Greubel, Apr 30 2018

Mathematica

CoefficientList[Series[(1+x-x^2-Sqrt[1-10x-x^2+10x^3+x^4])/(6x(1-x^2)),{x,0,20}],x] (* Harvey P. Dale, Aug 12 2011 *)

PARI

x='x+O('x^30); Vec((1+x-x^2-sqrt(1-10*x-x^2+10*x^3+x^4))/(6*x*(1-x^2))) \\ G. C. Greubel, Apr 30 2018

Formula

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

G.f.: 1/(1-2x-x^2-6x^2/(1-5x-x^2-6x^2/(1-5x-x^2-6x^2/(1-5-x^2-6x^2/(1-... (continued fraction).

a(n) = Sum_{k=0..floor(n/2)} C(n-k,k)*A107841(n-2*k).

Recurrence: (n+1)*a(n) = (n-5)*a(n-6) + 5*(2*n-7)*a(n-5) - (2*n-7)*a(n-4) - 20*(n-2)*a(n-3) + (2*n-1)*a(n-2) + 5*(2*n-1)*a(n-1). - R. J. Mathar, Jul 24 2012, simplified by Fung Lam, Jan 27 2014

a(n) ~ r*(r+10) * sqrt(10*r^3-2*r^2-30*r+4) / (12 * sqrt(Pi) * n^(3/2) * r^(n+1)), where r = 1 / (5/2 + sqrt(6) + 1/2*sqrt(53+20*sqrt(6))) = 0.100010105114224353... - Vaclav Kotesovec, Feb 27 2014