OFFSET
0,3
FORMULA
G.f.: A(x) = 2 / (1-x^3+sqrt((1-x^3)^2-4*x)).
a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k+1,k) * binomial(2*n-5*k,n-3*k)/(n-2*k+1).
D-finite with recurrence (n+1)*a(n) +2*(-2*n+1)*a(n-1) +(-2*n+7)*a(n-3) +(n-8)*a(n-6)=0. - R. J. Mathar, Dec 04 2023
MAPLE
A367056 := proc(n)
add(binomial(n-2*k+1, k) * binomial(2*n-5*k, n-3*k)/(n-2*k+1), k=0..floor(n/3)) ;
end proc:
seq(A367056(n), n=0..70) ; # R. J. Mathar, Dec 04 2023
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(n-2*k+1, k)*binomial(2*n-5*k, n-3*k)/(n-2*k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 04 2023
STATUS
approved