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 A382649 #13 May 16 2025 19:29:00
%S A382649 1,2,15,52,213,834,3043,11576,41601,152458,544039,1950132,6895773,
%T A382649 24403302,85542339,300101048,1044436937,3639851814,12594713911,
%U A382649 43660404108,150357976533,518991977194,1780132570723,6122965091976,20928650616113,71779065646510,244590689773839
%N A382649 Expansion of 1/(1 - x*(1 + 4*x)^(3/2))^2.
%C A382649 a(82) is negative.
%H A382649 Vincenzo Librandi, <a href="/A382649/b382649.txt">Table of n, a(n) for n = 0..600</a>
%F A382649 a(n) = Sum_{k=0..n} 4^(n-k) * (k+1) * binomial(3*k/2,n-k).
%t A382649 Table[Sum[4^(n-k)* (k+1)* Binomial[3*k/2, n-k],{k,0,n}],{n,0,28}] (* _Vincenzo Librandi_, May 13 2025 *)
%o A382649 (PARI) a(n) = sum(k=0, n, 4^(n-k)*(k+1)*binomial(3*k/2, n-k));
%o A382649 (Magma) R<x>:=PowerSeriesRing(Rationals(), 28); Coefficients(R!( 1/(1 - x*(1 + 4*x)^(3/2))^2)); // _Vincenzo Librandi_, May 13 2025
%Y A382649 Cf. A382536, A382650.
%K A382649 sign,easy
%O A382649 0,2
%A A382649 _Seiichi Manyama_, Apr 02 2025