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 A127946 #27 Sep 08 2022 08:45:29
%S A127946 1,-6,-108,5832,944784,-459165024,-669462604992,2928229434235008,
%T A127946 38424226636031774976,-1512608105754026853705216,
%U A127946 -178635992073339063368878599168,63289660175631590117213474413627392,67269440586795655766964092111705109663744
%N A127946 Hankel transform of central coefficients of (1+k*x-3x^2)^n, k arbitrary integer.
%C A127946 Hankel transform of A098333. The Hankel transform of e.g.f. Bessel_I(0,2*sqrt(-3)x) and its k-th binomial transforms, are given by a(n). In general, the Hankel transform of e.g.f. Bessel_I(0,2*sqrt(m)x) and its binomial transforms is 2^n*m^C(n+1,2).
%C A127946 Let T_n denote the n X n matrix with T_n(i,j) = 3^min(i,j); then a(n) = ((-1)^floor((n+1)/2))*det(T_(n+1))/3. - _Lechoslaw Ratajczak_, May 16 2021
%H A127946 G. C. Greubel, <a href="/A127946/b127946.txt">Table of n, a(n) for n = 0..63</a>
%F A127946 a(n) = (cos(Pi*n/2) - sin(Pi*n/2))*6^n*3^C(n,2) = 2^n*(-3)^C(n+1,2).
%t A127946 A127946[0] = 1; A127946[n_] := {1, -1, -1, 1}[[Mod[n, 4] + 1]] * 2^n * 3^(n(n + 1)/2); Table[A127946[n], {n, 0, 12}] (* _Jean-François Alcover_, Oct 04 2016 *)
%t A127946 Table[2^n*(-3)^Binomial[n+1,2], {n,0,30}] (* _G. C. Greubel_, May 03 2018 *)
%o A127946 (PARI) a(n)=if((n-1)%4<2,-1,1)*2^n*3^(n*(n+1)/2) \\ _Charles R Greathouse IV_, Oct 04 2016
%o A127946 (Magma) [2^n*(-3)^Binomial(n+1,2): n in [0..30]]; // _G. C. Greubel_, May 03 2018
%Y A127946 a(n) = A083667(n+1)/2.
%K A127946 easy,sign
%O A127946 0,2
%A A127946 _Paul Barry_, Feb 08 2007