OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: 1 / ( sqrt(1-4*x) * (1 + x^2) ).
a(n) ~ 2^(2*n + 4) / (17*sqrt(Pi*n)). - Vaclav Kotesovec, Jan 29 2023
D-finite with recurrence n*a(n) +2*(-2*n+1)*a(n-1) +n*a(n-2) +2*(-2*n+1)*a(n-3)=0. - R. J. Mathar, Mar 12 2023
a(n)+a(n-2) = A000984(n). - R. J. Mathar, Mar 12 2023
MAPLE
A360185 := proc(n)
add((-1)^k*binomial(2*n-4*k, n-2*k), k=0..n/2) ;
end proc:
seq(A360185(n), n=0..70) ; # R. J. Mathar, Mar 12 2023
PROG
(PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(2*n-4*k, n-2*k));
(PARI) my(N=30, x='x+O('x^N)); Vec(1/(sqrt(1-4*x)*(1+x^2)))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jan 29 2023
STATUS
approved