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 A387211 #16 Aug 23 2025 09:56:13
%S A387211 1,8,58,400,2678,17584,113892,730272,4646310,29380912,184867148,
%T A387211 1158418144,7233806524,45038743520,279704675464,1733203476288,
%U A387211 10718950211334,66176597723184,407931346057020,2511127341708384,15438601388617044,94810212917983392,581639541983344632
%N A387211 Expansion of sqrt((1-2*x) / (1-6*x)^3).
%H A387211 Vincenzo Librandi, <a href="/A387211/b387211.txt">Table of n, a(n) for n = 0..500</a>
%F A387211 n*a(n) = 8*n*a(n-1) - 12*(n-1)*a(n-2) for n > 1.
%F A387211 a(n) = (1/2)^n * Sum_{k=0..n} 3^k * (2*k+1) * binomial(2*k,k) * binomial(2*(n-k),n-k)/(1-2*(n-k)).
%F A387211 a(n) = Sum_{k=0..n} 2^(n-k) * (2*k+1) * binomial(2*k,k) * binomial(n,n-k).
%F A387211 a(n) = Sum_{k=0..n} (-1)^k * 6^(n-k) * binomial(2*k,k)/(1-2*k) * binomial(n,n-k).
%t A387211 CoefficientList[Series[Sqrt[(1-2*x)/(1-6*x)^3],{x,0,33}],x] (* _Vincenzo Librandi_, Aug 23 2025 *)
%o A387211 (PARI) my(N=30, x='x+O('x^N)); Vec(sqrt((1-2*x)/(1-6*x)^3))
%o A387211 (Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := Sqrt((1- 2*x) / (1-6*x)^3); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // _Vincenzo Librandi_, Aug 23 2025
%Y A387211 Cf. A163869, A387212.
%Y A387211 Cf. A360317.
%K A387211 nonn,new
%O A387211 0,2
%A A387211 _Seiichi Manyama_, Aug 22 2025