A358108 - OEIS

%I #12 Nov 13 2022 16:24:19

%S 1,20,420,9296,216868,5313360,135866640,3599688000,98122746660,

%T 2735243498960,77595234251920,2231860533960000,64904359322352400,

%U 1904342118510144320,56285527873777258560,1673824975976543421696,50036226313229526706980,1502471400349641645458640

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

%C Belongs to the family of Apéry-like sequences.

%F a(n) = 16^n * hypergeom([1/2, 1/2, -n], [1, 1], -1).

%F a(n) ~ 2^(5*n + 1) / (Pi*n). - _Vaclav Kotesovec_, Nov 12 2022

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

%p seq(a(n), n = 0..17);

%t a[n_] := 16^n * HypergeometricPFQ[{1/2, 1/2, -n}, {1, 1}, -1]; Array[a, 18, 0] (* _Amiram Eldar_, Nov 12 2022 *)

%o (Python)

%o from sympy import binomial, S

%o def A358108(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 Cf. A143583.

%K nonn

%O 0,2

%A _Peter Luschny_, Nov 12 2022