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 A374508 #18 Aug 23 2025 09:53:01
%S A374508 1,5,5,-35,-140,-84,840,2640,495,-16445,-41041,11375,282100,559300,
%T A374508 -474300,-4399260,-6807225,11062275,63677075,73363675,-208411280,
%U A374508 -865816600,-665544100,3475847700,11129861925,4130560161,-53332660395,-135538728395,9634906640
%N A374508 Expansion of 1/(1 - 2*x + 5*x^2)^(5/2).
%F A374508 a(0) = 1, a(1) = 5; a(n) = ((2*n+3)*a(n-1) - 5*(n+3)*a(n-2))/n.
%F A374508 a(n) = (binomial(n+4,2)/6) * Sum_{k=0..floor(n/2)} (-1)^k * binomial(n+2,n-2*k) * binomial(2*k+2,k).
%F A374508 a(n) = Pochhammer(n+1, 4)*hypergeom([(1-n)/2, -n/2], [3], -4)/4!. - _Stefano Spezia_, Jul 10 2024
%F A374508 a(n) = (-1)^n * Sum_{k=0..n} 2^k * (5/2)^(n-k) * binomial(-5/2,k) * binomial(k,n-k). - _Seiichi Manyama_, Aug 23 2025
%t A374508 a[n_]:= Pochhammer[n+1, 4]*Hypergeometric2F1[(1-n)/2, -n/2, 3, -4]/4!; Array[a,29,0] (* _Stefano Spezia_, Jul 10 2024 *)
%o A374508 (PARI) a(n) = binomial(n+4, 2)/6*sum(k=0, n\2, (-1)^k*binomial(n+2, n-2*k)*binomial(2*k+2, k));
%Y A374508 Cf. A098331, A102840, A374509.
%Y A374508 Cf. A245551.
%K A374508 sign,changed
%O A374508 0,2
%A A374508 _Seiichi Manyama_, Jul 09 2024