OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
Generally for G.f. = 2/(1-x+sqrt(1-2x-(4*z-1)*x^2)) is asymptotic
a(n) ~ (1+2*sqrt(z))^(n+3/2)/(2*sqrt(Pi)*z^(3/4)*n^(3/2)); here we have the case z=7.
D-finite with recurrence: (n+2)*a(n)=(2*n+1)*a(n-1)+(4*z-1)*(n-1)*a(n-2);; here with z=7.
G.f.: 1/(1 - x - 7*x^2/(1 - x - 7*x^2/(1 - x - 7*x^2/(1 - x - 7*x^2/(1 - ....))))), a continued fraction. - Ilya Gutkovskiy, May 26 2017
MATHEMATICA
Table[SeriesCoefficient[2/(1-x+Sqrt[1-2*x-27*x^2]), {x, 0, n}], {n, 0, 25}]
Table[Sum[Binomial[n, 2k]*Binomial[2k, k]*7^k/(k+1), {k, 0, n}], {n, 0, 25}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Sep 29 2012
STATUS
approved