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 A382536 #24 Apr 13 2025 03:02:10
%S A382536 1,1,7,19,63,221,679,2365,7499,25351,82043,274031,892263,2972127,
%T A382536 9686899,32261819,105124711,350277365,1140610399,3803874525,
%U A382536 12372800403,41319077557,134176480535,448958154449,1454582791283,4879992151217,15762304059447,53067612190093
%N A382536 Expansion of 1/(1 - x*(1 + 4*x)^(3/2)).
%C A382536 a(62) is negative.
%H A382536 Vincenzo Librandi, <a href="/A382536/b382536.txt">Table of n, a(n) for n = 0..400</a>
%F A382536 a(n) = Sum_{k=0..n} 4^(n-k) * binomial(3*k/2,n-k).
%F A382536 D-finite with recurrence (-n+1)*a(n) +2*(-2*n+7)*a(n-1) +(n-1)*a(n-2) +2*(8*n-13)*a(n-3) +24*(4*n-9)*a(n-4) +32*(8*n-23)*a(n-5) +128*(2*n-7)*a(n-6)=0. - _R. J. Mathar_, Apr 02 2025
%F A382536 a(n) ~ 3 * (-1)^(n+1) * 2^(2*n-4) / (sqrt(Pi) * n^(5/2)). - _Vaclav Kotesovec_, Apr 13 2025
%t A382536 Table[Sum[4^(n-k)*Binomial[3*k/2,n-k],{k,0,n}],{n,0,35}] (* _Vincenzo Librandi_, Apr 01 2025 *)
%o A382536 (PARI) a(n) = sum(k=0, n, 4^(n-k)*binomial(3*k/2, n-k));
%o A382536 (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 01 2025
%Y A382536 Cf. A362154, A382537, A382538.
%Y A382536 Cf. A002421, A382514.
%K A382536 sign,easy
%O A382536 0,3
%A A382536 _Seiichi Manyama_, Mar 31 2025