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 A382541 #16 May 12 2025 19:20:43
%S A382541 1,2,15,100,645,4098,25795,161256,1002513,6203434,38230951,234774948,
%T A382541 1437193101,8773022374,53416562787,324488659784,1967025910873,
%U A382541 11901070329414,71878009609591,433411746865948,2609477469570885,15689257525890666,94208451895149123
%N A382541 Expansion of 1/(1 - x/(1 - 4*x)^(3/2))^2.
%H A382541 Vincenzo Librandi, <a href="/A382541/b382541.txt">Table of n, a(n) for n = 0..600</a>
%F A382541 a(n) = Sum_{k=0..n} 4^(n-k) * (k+1) * binomial(n+k/2-1,n-k).
%F A382541 D-finite with recurrence (-n+1)*a(n) +2*(8*n-13)*a(n-1) +(-95*n+217)*a(n-2) +2*(126*n-359)*a(n-3) +128*(-2*n+7)*a(n-4)=0. - _R. J. Mathar_, Apr 02 2025
%t A382541 Table[Sum[(4)^(n-k)* (k+1)* Binomial[n+k/2-1,n-k],{k,0,n}],{n,0,30}] (* _Vincenzo Librandi_, May 12 2025 *)
%o A382541 (PARI) a(n) = sum(k=0, n, 4^(n-k)*(k+1)*binomial(n+k/2-1, n-k));
%o A382541 (Magma) R<x>:=PowerSeriesRing(Rationals(), 25); Coefficients(R!( 1/(1 - x/(1-4*x)^(3/2))^2)); // _Vincenzo Librandi_, May 12 2025
%Y A382541 Cf. A382514, A382542.
%Y A382541 Cf. A382539.
%K A382541 nonn,easy
%O A382541 0,2
%A A382541 _Seiichi Manyama_, Mar 31 2025