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A360185
a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(2*n-4*k,n-2*k).
5
1, 2, 5, 18, 65, 234, 859, 3198, 12011, 45422, 172745, 660010, 2531411, 9740590, 37585189, 145376930, 563495201, 2188229290, 8511640099, 33157034510, 129334888721, 505100839930, 1974764074999, 7728329887670, 30272839608101, 118682276550082, 465645693340003
OFFSET
0,2
LINKS
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
Sequence in context: A093635 A354420 A024025 * A084518 A150014 A150015
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jan 29 2023
STATUS
approved