OFFSET
0,2
FORMULA
G.f.: (288*x^2*cos(arcsin(216*x^2-1)/3))/(sqrt(432*x^2-46656*x^4)*(2*sin(arcsin(216*x^2-1)/3)+1)).
Conjecture: D-finite with recurrence n*(n-1)*a(n) -12*(3*n-2)*(3*n-4)*a(n-2)=0. - R. J. Mathar, Mar 06 2022
MAPLE
a:= n-> ceil(4^n*binomial(3*n/2, n)/3):
seq(a(n), n=0..20); # Alois P. Heinz, Oct 25 2021
MATHEMATICA
a[n_] := If[EvenQ[n], 4^n * Binomial[3*n/2 - 1, n], Binomial[(3*n - 1)/2, n] * Binomial[3*n - 1, (3*n - 1)/2] / Binomial[n - 1, (n - 1)/2]]; Array[a, 18, 0] (* Amiram Eldar, Oct 25 2021 *)
PROG
(Maxima)
a(n):=if evenp(n) then 4^n*binomial(3*n/2-1, n) else ((binomial((3*n-1)/2, n))*
(binomial(3*n-1, (3*n-1)/2)))/binomial(n-1, (n-1)/2);
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Oct 25 2021
STATUS
approved