This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A358109 #11 Nov 13 2022 16:24:27
%S A358109 1,20,388,7376,138340,2572880,47652240,882388800,16402291620,
%T A358109 307411770320,5837516987920,112918906836800,2237687548230160,
%U A358109 45677390764531520,964818477552462400,21148251536958233856,481370160754727691300,11360399185583414128848,277079154699775861823376
%N A358109 a(n) = 16^n * Sum_{k=0..n} binomial(1/2, k)^2 * binomial(n, k).
%C A358109 Belongs to the family of Apéry-like sequences.
%F A358109 a(n) = 16^n * hypergeom([-1/2, -1/2, -n], [1, 1], -1).
%F A358109 a(n) ~ 2^(5*n + 1) / (Pi * n^3). - _Vaclav Kotesovec_, Nov 12 2022
%p A358109 a := n -> 16^n*add(binomial(1/2, k)^2*binomial(n, k), k = 0..n):
%p A358109 seq(a(n), n = 0..18);
%t A358109 a[n_] := 16^n * HypergeometricPFQ[{-1/2, -1/2, -n}, {1, 1}, -1]; Array[a, 19, 0] (* _Amiram Eldar_, Nov 12 2022 *)
%o A358109 (Python)
%o A358109 from sympy import binomial, S
%o A358109 def A358109(n): return (1<<(n<<2))*sum(binomial(S.Half,k)**2*binomial(n,k) for k in range(n+1)) # _Chai Wah Wu_, Nov 13 2022
%Y A358109 Cf. A358108, A143583.
%K A358109 nonn
%O A358109 0,2
%A A358109 _Peter Luschny_, Nov 12 2022