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 A382539 #17 May 13 2025 02:42:17
%S A382539 1,2,7,28,117,498,2139,9232,39953,173162,751103,3259132,14142973,
%T A382539 61367542,266223083,1154592752,5005724185,21694354406,93985418399,
%U A382539 407009142836,1761880487509,7623911365210,32976925264827,142585750821408,616281411472257,2662702949358158
%N A382539 Expansion of 1/(1 - x/(1 - 4*x)^(1/2))^2.
%H A382539 Vincenzo Librandi, <a href="/A382539/b382539.txt">Table of n, a(n) for n = 0..600</a>
%F A382539 a(n) = Sum_{k=0..n} 4^(n-k) * (k+1) * binomial(n-k/2-1,n-k).
%F A382539 D-finite with recurrence (-n+1)*a(n) +2*(4*n-7)*a(n-1) +(-15*n+41)*a(n-2) +2*(-2*n+3)*a(n-3)=0. - _R. J. Mathar_, Apr 02 2025
%t A382539 Table[Sum[4^(n-k)* (k+1)* Binomial[n-k/2-1, n-k],{k,0,n}],{n,0,25}] (* _Vincenzo Librandi_, May 13 2025 *)
%o A382539 (PARI) a(n) = sum(k=0, n, 4^(n-k)*(k+1)*binomial(n-k/2-1, n-k));
%o A382539 (Magma) R<x>:=PowerSeriesRing(Rationals(), 25); Coefficients(R!( 1/(1 - x/(1 - 4*x)^(1/2))^2)); // _Vincenzo Librandi_, May 13 2025
%Y A382539 Cf. A026671, A382540.
%K A382539 nonn,easy
%O A382539 0,2
%A A382539 _Seiichi Manyama_, Mar 31 2025