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 A374509 #17 Aug 23 2025 09:50:18
%S A374509 1,7,14,-42,-294,-462,1386,7722,9009,-37037,-160160,-123760,835380,
%T A374509 2848860,1046520,-16550520,-45140865,3533145,296447690,648593330,
%U A374509 -393463070,-4895709390,-8489647530,10975099590,75528298755,100311659721,-230350834728,-1097798696456
%N A374509 Expansion of 1/(1 - 2*x + 5*x^2)^(7/2).
%F A374509 a(0) = 1, a(1) = 7; a(n) = ((2*n+5)*a(n-1) - 5*(n+5)*a(n-2))/n.
%F A374509 a(n) = (binomial(n+6,3)/20) * Sum_{k=0..floor(n/2)} (-1)^k * binomial(n+3,n-2*k) * binomial(2*k+3,k).
%F A374509 a(n) = Pochhammer(n+1, 6)*hypergeom([(1-n)/2, -n/2], [4], -4)/6!. - _Stefano Spezia_, Jul 10 2024
%F A374509 a(n) = (-1)^n * Sum_{k=0..n} 2^k * (5/2)^(n-k) * binomial(-7/2,k) * binomial(k,n-k). - _Seiichi Manyama_, Aug 23 2025
%t A374509 a[n_]:= Pochhammer[n+1, 6]*Hypergeometric2F1[(1-n)/2, -n/2, 4, -4]/6!; Array[a,28,0] (* _Stefano Spezia_, Jul 10 2024 *)
%o A374509 (PARI) a(n) = binomial(n+6, 3)/20*sum(k=0, n\2, (-1)^k*binomial(n+3, n-2*k)*binomial(2*k+3, k));
%Y A374509 Cf. A098331, A102840, A374508.
%Y A374509 Cf. A374506.
%K A374509 sign,changed
%O A374509 0,2
%A A374509 _Seiichi Manyama_, Jul 09 2024