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 A371399 #11 Mar 22 2024 14:54:28
%S A371399 1,2,12,60,340,1932,11256,66264,394020,2359500,14211912,86004360,
%T A371399 522502344,3184844600,19467675120,119288938800,732508344516,
%U A371399 4506518476620,27771180181800,171393806476200,1059200506065240,6553715347503720,40595235803924880,251709010315822800
%N A371399 a(n) = 2^n * Sum_{k=0..n} binomial(k + n, k) * binomial(2*n - k, n) * (-1/2)^k.
%F A371399 a(n) = 2^n * Sum_{k=0..n} A371400(n, k) * (-1/2)^k.
%F A371399 a(n) = 2^n * binomial(2*n, n) * hypergeom([-n, 1 + n], [-2*n], -1/2).
%p A371399 seq((2^n*add(binomial(k+n, k)*binomial(2*n-k, n)*(-1/2)^k, k=0..n)), n=0..23);
%t A371399 a[n_] := 2^n Binomial[2 n, n] Hypergeometric2F1[-n, 1 + n, -2 n, -1/2];
%t A371399 Table[a[n], {n, 0, 23}]
%o A371399 (Python)
%o A371399 from math import comb
%o A371399 def A371399(n): return sum(comb(k+n,k)*comb((n<<1)-k,n)*(-1 if k&1 else 1)<<n-k for k in range(n+1)) # _Chai Wah Wu_, Mar 22 2024
%Y A371399 Cf. A371400.
%K A371399 nonn
%O A371399 0,2
%A A371399 _Peter Luschny_, Mar 21 2024