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 A382332 #28 May 12 2025 13:59:52
%S A382332 1,14,154,1470,12866,106078,837018,6385262,47420674,344553902,
%T A382332 2458367898,17272647966,119770278978,821068784382,5572735854234,
%U A382332 37490757508302,250247764120578,1658681038111566,10924592141535898,71541334475749502,466060971286552642
%N A382332 Expansion of 1/(1 - 4*x/(1-x)^2)^(7/2).
%H A382332 Vincenzo Librandi, <a href="/A382332/b382332.txt">Table of n, a(n) for n = 0..600</a>
%F A382332 a(0) = 1; a(n) = 2 * Sum_{k=0..n-1} (7-5*k/n) * (n-k) * a(k).
%F A382332 a(n) = ((7*n+7)*a(n-1) - (7*n-28)*a(n-2) + (n-3)*a(n-3))/n for n > 2.
%F A382332 a(n) = Sum_{k=0..n} (-4)^k * binomial(-7/2,k) * binomial(n+k-1,n-k).
%F A382332 a(n) = 14*n*hypergeom([9/2, 1-n, 1+n], [3/2, 2], -1) for n > 0. - _Stefano Spezia_, Mar 30 2025
%F A382332 a(n) ~ 2^(5/4) * (1 + sqrt(2))^(2*n) * n^(5/2) / (15*sqrt(Pi)). - _Vaclav Kotesovec_, May 03 2025
%t A382332 Table[Sum[(-4)^k* Binomial[-7/2,k]*Binomial[n+k-1, n-k],{k,0,n}],{n,0,30}] (* _Vincenzo Librandi_, May 12 2025 *)
%o A382332 (PARI) a(n) = sum(k=0, n, (-4)^k*binomial(-7/2, k)*binomial(n+k-1, n-k));
%o A382332 (Magma) R<x>:=PowerSeriesRing(Rationals(), 25); Coefficients(R!( 1/(1 - 4*x/(1-x)^2)^(7/2))); // _Vincenzo Librandi_, May 12 2025
%Y A382332 Cf. A110170, A377198, A382274.
%Y A382332 Cf. A020918, A377200.
%K A382332 nonn
%O A382332 0,2
%A A382332 _Seiichi Manyama_, Mar 30 2025