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 A382514 #18 Apr 09 2025 23:40:05
%S A382514 1,1,7,43,255,1493,8695,50517,293163,1700335,9859019,57156631,
%T A382514 331332423,1920621431,11132911939,64531189379,374047777319,
%U A382514 2168115796941,12567146992975,72843402779669,422224417571347,2447350774345341,14185640454054279,82224565359415849
%N A382514 Expansion of 1/(1 - x/(1 - 4*x)^(3/2)).
%H A382514 Vincenzo Librandi, <a href="/A382514/b382514.txt">Table of n, a(n) for n = 0..300</a>
%F A382514 a(n) = Sum_{k=0..n} 4^(n-k) * binomial(n+k/2-1,n-k).
%F A382514 D-finite with recurrence (-n+1)*a(n) +2*(8*n-13)*a(n-1) +5*(-19*n+43)*a(n-2) +2*(126*n-361)*a(n-3) +128*(-2*n+7)*a(n-4)=0. - _R. J. Mathar_, Mar 31 2025
%t A382514 Table[Sum[4^(n-k)*Binomial[n+k/2-1,n-k],{k,0,n}],{n,0,35}] (* _Vincenzo Librandi_, Apr 09 2025 *)
%o A382514 (PARI) a(n) = sum(k=0, n, 4^(n-k)*binomial(n+k/2-1, n-k));
%o A382514 (Magma) R<x> := PowerSeriesRing(Rationals(), 40); f := 1/(1 - x/(1 - 4*x)^(3/2)); seq := [ Coefficient(f, n) : n in [0..30] ]; seq; // _Vincenzo Librandi_, Apr 09 2025
%Y A382514 Cf. A026671, A382515.
%Y A382514 Cf. A002457.
%K A382514 nonn,easy
%O A382514 0,3
%A A382514 _Seiichi Manyama_, Mar 30 2025