A245924 - OEIS

%I #13 Jan 30 2020 21:29:17

%S 1,18,279,4132,59949,860022,12252547,173756232,2456093529,34634926810,

%T 487525847535,6852798238572,96216461002117,1349689029354558,

%U 18918661407653979,265016591806251664,3710426585319049905,51924984423522889122,726369947645489367751,10157588028419864394420

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

%C Self-convolution of A245927.

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

%H G. C. Greubel, <a href="/A245924/b245924.txt">Table of n, a(n) for n = 0..870</a>

%F 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

%F 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

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

%t 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 *)

%o (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)}

%o for(n=0, 20, print1(a(n), ", "))

%Y Cf. A245923, A245927.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Aug 16 2014