OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Hacène Belbachir, Abdelghani Mehdaoui, László Szalay, Diagonal Sums in the Pascal Pyramid, II: Applications, J. Int. Seq., Vol. 22 (2019), Article 19.3.5.
Vaclav Kotesovec, Graph - the asymptotic ratio
FORMULA
G.f.: 1/(1-12*x+48*x^2)^(1/2).
E.g.f.: exp(6*x)*BesselJ(0,2*sqrt(3)*x).
If mod(n,6)=4 then a(n) ~ (-1)^((n+8)/6) * 3^((n+1)/2) * 4^(n-1) / (sqrt(Pi) * n^(3/2)), else a(n) ~ 3^(n/2) * 2^(2*n+1) * cos(Pi*(n-1)/6) / sqrt(Pi*n). - Vaclav Kotesovec, Jun 08 2015
D-finite with recurrence n*a(n) +6*(-2*n+1)*a(n-1) +48*(n-1)*a(n-2)=0. [Belbachir]
MATHEMATICA
CoefficientList[Series[1/(1-12*x+48*x^2)^(1/2), {x, 0, 20}], x] (* Vaclav Kotesovec, Jun 08 2015 *)
PROG
(PARI) Vec(1/(1-12*x+48*x^2)^(1/2) + x^50) \\ G. C. Greubel, Feb 14 2017
CROSSREFS
KEYWORD
sign
AUTHOR
Sergei N. Gladkovskii, Jun 08 2015
STATUS
approved