A358362 a(n) = 16^n * Sum_{k=0..n} (-1)^k*binomial(-1/2, k)^2.

1, 12, 228, 3248, 56868, 846384, 14395920, 218556096, 3662534436, 56236646576, 933921124752, 14445103689408, 238434118702864, 3706773418885824, 60917716297733184, 950622015752780544, 15571249887287040804, 243694280206569964464, 3981466564018425521424

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = (64*(2*n - 1)^2*a(n - 2) + (16*n - 4)*a(n - 1)) / n^2.

G.f.: hypergeom([1/2, 1/2], [1], -16*x)/(16*x - 1).

G.f.: 2*EllipticK(4*I*sqrt(x))/(Pi*(1 - 16*x)).

a(n) ~ A014549 * 2^(4*n). - Vaclav Kotesovec, Nov 14 2023

Maple

a := n -> 16^n*add((-1)^k*binomial(-1/2, k)^2, k = 0..n):
seq(a(n), n = 0..19);

Mathematica

a[n_] := 16^n * Sum[(-1)^k*Binomial[-1/2, k]^2, {k, 0, n}]; Array[a, 19, 0] (* Amiram Eldar, Nov 12 2022 *)

Crossrefs

Cf. A358363, A358364, A358365, A367330.

Sequence in context: A300561 A358948 A361184 * A337332 A290754 A318417

Adjacent sequences: A358359 A358360 A358361 * A358363 A358364 A358365

Keyword

nonn

Author

Peter Luschny, Nov 12 2022

Status

approved