OFFSET
0,2
FORMULA
a(n) = (-64*(2*n - 1)^2*a(n - 2) + 4*(8*n^2 - 4*n + 1)*a(n - 1)) / n^2.
G.f.: hypergeom([1/2, 1/2], [1], 16*x)/(1 - 16*x).
G.f.: 2*EllipticK(4*sqrt(x))/(Pi*(1 - 16*x)).
a(n) ~ (log(n) + gamma + 4*log(2)) * 2^(4*n)/Pi, where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Nov 14 2023
MAPLE
a := n -> 16^n*add(binomial(-1/2, k)^2, k = 0..n):
seq(a(n), n = 0..18);
MATHEMATICA
a[n_] := 16^n * Sum[Binomial[-1/2, k]^2, {k, 0, n}]; Array[a, 19, 0] (* Amiram Eldar, Nov 12 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Nov 12 2022
STATUS
approved