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 A127945 #13 Sep 08 2022 08:45:29
%S A127945 1,-4,-32,512,16384,-1048576,-134217728,34359738368,17592186044416,
%T A127945 -18014398509481984,-36893488147419103232,151115727451828646838272,
%U A127945 1237940039285380274899124224,-20282409603651670423947251286016
%N A127945 Hankel transform of central coefficients of (1+k*x-2x^2)^n, k arbitrary integer.
%C A127945 Hankel transform of A098332. The Hankel transform of e.g.f. Bessel_I(0,2*sqrt(-2)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 A127945 Unsigned version is A036442. - _Philippe Deléham_, Dec 11 2008
%H A127945 G. C. Greubel, <a href="/A127945/b127945.txt">Table of n, a(n) for n = 0..79</a>
%F A127945 a(n) = (cos(Pi*n/2) - sin(Pi*n/2))*4^n*2^C(n,2).
%F A127945 a(n) = 2^n*(-2)^C(n+1,2).
%t A127945 Table[2^n*(-2)^Binomial[n+1,2], {n, 0, 25}] (* _G. C. Greubel_, May 01 2018 *)
%o A127945 (PARI) for(n=0,25, print1(2^n*(-2)^binomial(n+1,2), ", ")) \\ _G. C. Greubel_, May 01 2018
%o A127945 (Magma) [2^n*(-2)^Binomial(n+1,2): n in [0..25]]; // _G. C. Greubel_, May 01 2018
%Y A127945 Cf. A036442, A098332.
%K A127945 easy,sign
%O A127945 0,2
%A A127945 _Paul Barry_, Feb 08 2007