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

0,2

Links

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

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

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 *)

Prog

(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
(Magma) m:=25; R<x>:=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

Crossrefs

Sequence in context: A039632 A143816 A220783 * A185627 A216585 A245277

Adjacent sequences: A160849 A160850 A160851 * A160853 A160854 A160855

Keyword

easy,nonn

Author

Paul Barry, May 28 2009

Status

approved