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 A377199 #21 May 10 2025 23:13:28
%S A377199 1,10,80,570,3790,24062,147780,885190,5199560,30065870,171623328,
%T A377199 969151710,5422863630,30105497970,165993714540,909770119914,
%U A377199 4959840748350,26912374137150,145411035749600,782681600883950,4198276264607290,22448626776903450,119690255236279100
%N A377199 Expansion of 1/(1 - 4*x/(1-x))^(5/2).
%H A377199 Vincenzo Librandi, <a href="/A377199/b377199.txt">Table of n, a(n) for n = 0..500</a>
%F A377199 a(0) = 1; a(n) = 2 * Sum_{k=0..n-1} (5-3*k/n) * a(k).
%F A377199 a(n) = (2*(3*n+2)*a(n-1) - 5*(n-2)*a(n-2))/n for n > 1.
%F A377199 a(n) = Sum_{k=0..n} (-4)^k * binomial(-5/2,k) * binomial(n-1,n-k).
%F A377199 a(n) ~ 128 * n^(3/2) * 5^(n - 5/2) / (3*sqrt(Pi)). - _Vaclav Kotesovec_, Oct 26 2024
%F A377199 a(n) = 10*hypergeom([7/2, 1-n], [2], -4) for n > 0. - _Stefano Spezia_, May 08 2025
%t A377199 Table[Sum[(-4)^k*Binomial[-5/2,k]*Binomial[n-1,n-k],{k,0,n}],{n,0,35}] (* _Vincenzo Librandi_, May 10 2025 *)
%o A377199 (PARI) a(n) = sum(k=0, n, (-4)^k*binomial(-5/2, k)*binomial(n-1, n-k));
%o A377199 (Magma) R<x>:=PowerSeriesRing(Rationals(), 35); Coefficients(R!( 1/(1 - 4*x/(1-x))^(5/2))); // _Vincenzo Librandi_, May 10 2025
%Y A377199 Cf. A085362, A377197, A377200.
%K A377199 nonn
%O A377199 0,2
%A A377199 _Seiichi Manyama_, Oct 19 2024