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 A374513 #16 Oct 19 2024 08:31:27
%S A374513 1,14,140,1176,8904,62832,421344,2718144,17008992,103847744,621292672,
%T A374513 3654187264,21182563584,121263109632,686660004864,3851149940736,
%U A374513 21416533501440,118199459288064,647926485764096,3529938203545600,19124354344775680
%N A374513 Expansion of 1/(1 - 4*x - 4*x^2)^(7/2).
%F A374513 a(0) = 1, a(1) = 14; a(n) = (2*(2*n+5)*a(n-1) + 4*(n+5)*a(n-2))/n.
%F A374513 a(n) = (binomial(n+6,3)/20) * Sum_{k=0..floor(n/2)} 2^(n-k) * binomial(n+3,n-2*k) * binomial(2*k+3,k).
%F A374513 a(n) = 2^(n-4)*Pochhammer(n+1, 6)*hypergeom([(1-n)/2, -n/2], [4], 2)/45. - _Stefano Spezia_, Jul 10 2024
%F A374513 a(n) = Sum_{k=0..n} (-4)^k * binomial(-7/2,k) * binomial(k,n-k). - _Seiichi Manyama_, Oct 19 2024
%t A374513 a[n_]:=2^(n-4) Pochhammer[n+1, 6]*Hypergeometric2F1[(1-n)/2, -n/2, 4, 2]/45; Array[a,21,0] (* _Stefano Spezia_, Jul 10 2024 *)
%o A374513 (PARI) a(n) = binomial(n+6, 3)/20*sum(k=0, n\2, 2^(n-k)*binomial(n+3, n-2*k)*binomial(2*k+3, k));
%Y A374513 Cf. A006139, A374497, A374511.
%K A374513 nonn
%O A374513 0,2
%A A374513 _Seiichi Manyama_, Jul 09 2024