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 A382647 #11 May 16 2025 19:28:50
%S A382647 1,2,7,12,37,50,187,128,1057,-502,7679,-14420,73453,-212554,843019,
%T A382647 -2848064,10602409,-37875706,139533151,-510006524,1885309253,
%U A382647 -6974175142,25940881947,-96731191728,361980829841,-1358121976978,5109416286295,-19267391982612
%N A382647 Expansion of 1/(1 - x*(1 + 4*x)^(1/2))^2.
%H A382647 Vincenzo Librandi, <a href="/A382647/b382647.txt">Table of n, a(n) for n = 0..600</a>
%F A382647 a(n) = Sum_{k=0..n} 4^(n-k) * (k+1) * binomial(k/2,n-k).
%t A382647 Table[Sum[4^(n-k)* (k+1)* Binomial[k/2, n-k],{k,0,n}],{n,0,28}] (* _Vincenzo Librandi_, May 13 2025 *)
%o A382647 (PARI) a(n) = sum(k=0, n, 4^(n-k)*(k+1)*binomial(k/2, n-k));
%o A382647 (Magma) R<x>:=PowerSeriesRing(Rationals(), 28); Coefficients(R!( 1/(1 - x*(1 + 4*x)^(1/2))^2)); // _Vincenzo Librandi_, May 13 2025
%Y A382647 Cf. A382539, A382649.
%K A382647 sign,easy
%O A382647 0,2
%A A382647 _Seiichi Manyama_, Apr 02 2025