OFFSET
0,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
FORMULA
a(n) ~ 2^(n - 1/2) * phi^((5*n + 3)/2) / (sqrt(Pi) * 5^(1/4) * n^(3/2)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Oct 04 2020
From Alexander Burstein, Nov 26 2021: (Start)
G.f.: A(x) = 1 + 2*x*A(x)*(1 + A(x)^2)/(1 + A(x)).
G.f.: A(-x*A(x)^2) = 1/A(x). (End)
D-finite with recurrence +n*(n+1)*(5*n-11) *a(n) +4*(-55*n^3 +231*n^2 -263*n +51)*a(n-2) -16*(n-3)*(n-4)*(5*n-1)*a(n-4)=0. - R. J. Mathar, Mar 25 2024
MAPLE
A138020 := proc(n)
option remember ;
if n < 5 then
op(n+1, [1, 2, 6, 24, 110]) ;
else
4*(-55*n^3 +231*n^2 -263*n +51)*procname(n-2) -16*(n-3)*(n-4)*(5*n-1)*procname(n-4) ;
-%/n/(n+1)/(5*n-11)
end if;
end proc:
seq(A138020(n), n=0..30) ; # R. J. Mathar, Sep 27 2024
MATHEMATICA
CoefficientList[y/.AsymptoticSolve[y^2-1-2x(y+y^3) ==0, y->1, {x, 0, 21}][[1]], x] - Alexander Burstein, Nov 26 2021
PROG
(PARI) a(n)=polcoeff((1/x)*serreverse(x*sqrt((1-2*x)/(1+2*x+x^2*O(x^n)))), n)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 28 2008
STATUS
approved