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 A374511 #17 Oct 19 2024 08:31:23
%S A374511 1,10,80,560,3640,22512,134400,781440,4451040,24939200,137865728,
%T A374511 753625600,4080643840,21916106240,116877312000,619457482752,
%U A374511 3265293719040,17128725519360,89462514606080,465434423336960,2412895587536896,12468681310412800,64242981906022400
%N A374511 Expansion of 1/(1 - 4*x - 4*x^2)^(5/2).
%F A374511 a(0) = 1, a(1) = 10; a(n) = (2*(2*n+3)*a(n-1) + 4*(n+3)*a(n-2))/n.
%F A374511 a(n) = (binomial(n+4,2)/6) * Sum_{k=0..floor(n/2)} 2^(n-k) * binomial(n+2,n-2*k) * binomial(2*k+2,k).
%F A374511 a(n) = 2^(n-3)*Pochhammer(n+1, 4)*hypergeom([(1-n)/2, -n/2], [3], 2)/3. - _Stefano Spezia_, Jul 10 2024
%F A374511 a(n) = Sum_{k=0..n} (-4)^k * binomial(-5/2,k) * binomial(k,n-k). - _Seiichi Manyama_, Oct 19 2024
%t A374511 a[n_]:=2^(n-3) Pochhammer[n+1, 4]*Hypergeometric2F1[(1-n)/2, -n/2, 3, 2]/3; Array[a,23,0] (* _Stefano Spezia_, Jul 10 2024 *)
%o A374511 (PARI) a(n) = binomial(n+4, 2)/6*sum(k=0, n\2, 2^(n-k)*binomial(n+2, n-2*k)*binomial(2*k+2, k));
%Y A374511 Cf. A006139, A374497, A374513.
%K A374511 nonn
%O A374511 0,2
%A A374511 _Seiichi Manyama_, Jul 09 2024