A358363 - OEIS

A358363

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

1, 12, 196, 3120, 50020, 799536, 12799632, 204724416, 3276326820, 52413049520, 838703348496, 13418125153472, 214703825630736, 3435088134123200, 54963617747611200, 879389273444524800, 14070604335190692900, 225124668703739770800, 3602061930346132909200

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OFFSET

0,2

LINKS

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

FORMULA

a(n) = (64*(2*n - 3)^2*a(n - 2) + 12*(4*n - 3)*a(n - 1)) / n^2.

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

a(n) ~ sqrt(Pi) * 2^(4*n + 5/2) / Gamma(1/4)^2. - 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..18);