A245924 Expansion of (1-x - sqrt(1 - 14*x + x^2)) / (6*x*(1 - 14*x + x^2)).

1, 18, 279, 4132, 59949, 860022, 12252547, 173756232, 2456093529, 34634926810, 487525847535, 6852798238572, 96216461002117, 1349689029354558, 18918661407653979, 265016591806251664, 3710426585319049905, 51924984423522889122, 726369947645489367751, 10157588028419864394420

Offset: 0

Author

Paul D. Hanna, Aug 16 2014

Keywords

• nonn

Comments

Self-convolution of A245927.

Limit a(n+1)/a(n) = 7 + 4*sqrt(3).

Examples

			G.f.: A(x) = 1 + 18*x + 279*x^2 + 4132*x^3 + 59949*x^4 + 860022*x^5 +...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..870

Crossrefs

Cf. A245923, A245927.

Programs

Mathematica

CoefficientList[Series[(1 - x - Sqrt[1 - 14*x + x^2])/(6*x*(1 - 14*x + x^2)), {x,0,50}], x] (* G. C. Greubel, Feb 14 2017 *)

PARI

{a(n)=polcoeff( (1-x - sqrt(1-14*x+x^2 +x^2*O(x^n))) / (6*x*(1-14*x+x^2 +x*O(x^n))), n)}
for(n=0, 20, print1(a(n), ", "))

Formula

a(n) ~ (26 + 15*sqrt(3)) * (7 + 4*sqrt(3))^n / 24 * (1 - 1/(3^(1/4)*sqrt(Pi*n/2))). - Vaclav Kotesovec, Aug 17 2014

D-finite with recurrence: (n+1)*a(n) +7*(-4*n-1)*a(n-1) +99*(2*n-1)*a(n-2) +7*(-4*n+5)*a(n-3) +(n-2)*a(n-4)=0. - R. J. Mathar, Jan 23 2020