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 A382648 #12 May 16 2025 19:29:11
%S A382648 1,3,12,28,87,171,522,810,2985,2583,18528,-5244,141875,-241815,
%T A382648 1393314,-3905782,16326069,-54884079,209607744,-752322624,2812050471,
%U A382648 -10351091321,38636724474,-143916146094,539225694641,-2023036045635,7615213571172,-28722320569796,108591659035131
%N A382648 Expansion of 1/(1 - x*(1 + 4*x)^(1/2))^3.
%H A382648 Vincenzo Librandi, <a href="/A382648/b382648.txt">Table of n, a(n) for n = 0..600</a>
%F A382648 a(n) = Sum_{k=0..n} 4^(n-k) * binomial(k+2,2) * binomial(k/2,n-k).
%t A382648 Table[Sum[4^(n-k)* Binomial[k+2,2]* Binomial[k/2, n-k],{k,0,n}],{n,0,28}] (* _Vincenzo Librandi_, May 13 2025 *)
%o A382648 (PARI) a(n) = sum(k=0, n, 4^(n-k)*binomial(k+2, 2)*binomial(k/2, n-k));
%o A382648 (Magma) R<x>:=PowerSeriesRing(Rationals(), 28); Coefficients(R!( 1/(1 - x*(1 + 4*x)^(1/2))^3)); // _Vincenzo Librandi_, May 13 2025
%Y A382648 Cf. A382540, A382650.
%K A382648 sign,easy
%O A382648 0,2
%A A382648 _Seiichi Manyama_, Apr 02 2025