OFFSET
0,2
FORMULA
G.f.: 1 / ( sqrt(1-4*x) * (1 + x^2 * c(x)) ), where c(x) is the g.f. of A000108.
a(n) ~ 2^(2*n+3) / (9*sqrt(Pi*n)). - Vaclav Kotesovec, Feb 18 2023
D-finite with recurrence 2*n*a(n) +(-5*n+2)*a(n-1) +(-11*n+12)*a(n-2) +2*(-n+5)*a(n-3) +(-7*n+2)*a(n-4) +2*(-2*n+5)*a(n-5)=0. - R. J. Mathar, Mar 02 2023
MAPLE
A360211 := proc(n)
add((-1)^k*binomial(2*n-3*k, n-2*k), k=0..floor(n/2)) ;
end proc:
seq(A360211(n), n=0..40) ; # R. J. Mathar, Mar 02 2023
PROG
(PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(2*n-3*k, n-2*k));
(PARI) my(N=30, x='x+O('x^N)); Vec(1/(sqrt(1-4*x)*(1+2*x^2/(1+sqrt(1-4*x)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 30 2023
STATUS
approved