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 A187791 #48 Jan 27 2020 04:36:15
%S A187791 1,2,2,8,8,8,16,16,16,16,128,128,128,128,128,256,256,256,256,256,256,
%T A187791 1024,1024,1024,1024,1024,1024,1024,2048,2048,2048,2048,2048,2048,
%U A187791 2048,2048,32768,32768,32768,32768,32768,32768,32768,32768,32768,65536,65536,65536,65536,65536,65536,65536,65536,65536,65536
%N A187791 Repeat n+1 times 2^A005187(n).
%C A187791 a(n) is the denominators of the antidiagonals of the Lorentz factor, which can be written A001790(n)/A046161(n), and its differences.
%C A187791 1, 1/2, 3/8, 5/16, 35/128, 63/256,... the Lorentz gamma factor,
%C A187791 -1/2, -1/8, -1/16, -5/128, -7/256, -21/1024, ... -A098597(n)/A046161(n+1),from the Lorentz (beta) factor,
%C A187791 3/8, 1/16, 3/128, 3/256, 7/1024, 9/2048,... A161200(n+2)/A046161(n+2),
%C A187791 -5/16, -5/128, -3/256, -5/1024, -5/2048, -45/32768,... A161202(n+3)/A046161(n+4),
%C A187791 35/128, 7/256, 7/1024, 5/2048, 35/32768, 35/65536, ...
%C A187791 -63/256, -21/1024, -9/2048, -45/32768, -35/65536, -63/262144, ... .
%C A187791 Like 1/n and A164555(n)/A027642(n), the Lorentz factor is an autosequence of the second kind. The first column is the signed sequence.
%C A187791 The main diagonal is (-1)^n *A001790(n)/A061549(n).
%C A187791 The Lorentz factor is the differences of (0, followed by A001803(n)) / (1, followed by A046161(n)).
%C A187791 PiSK(n-2)=(0, 0, followed by A001803(n)) / (1, 1, followed by A046161(n)) is also an autosequence of second kind.
%C A187791 Remember that an autosequence of the second kind is a sequence whose inverse binomial transform is the sequence signed, with its main diagonal being the double of its first upper diagonal. - _Paul Curtz_, Oct 13 2013
%H A187791 OEIS Wiki, <a href="https://oeis.org/wiki/Autosequence">Autosequence</a>
%H A187791 Wikipedia, <a href="http://en.wikipedia.org/wiki/Lorentz factor">Lorentz Factor</a>.
%F A187791 Repeat A046161(n) n+1 times. Triangle.
%e A187791 1,
%e A187791 2, 2,
%e A187791 8, 8, 8,
%e A187791 16, 16, 16, 16.
%t A187791 Flatten[Table[Denominator[Binomial[2n, n]/4^n], {n, 0, 19}, {n + 1}]] (* _Alonso del Arte_, Jan 07 2013 *)
%t A187791 (* Checking with the antidiagonals *) diff = Table[ Differences[ CoefficientList[ Series[1/Sqrt[1 - x], {x, 0, 9}], x], n], {n, 0, 9}]; Table[ diff[[n-k+1,k]] // Denominator,{n,0,10},{k,1,n}] // Flatten (* _Jean-François Alcover_, Jan 07 2013 *)
%t A187791 Flatten[Table[2^IntegerExponent[(2*n)!, 2], {n, 0, 19}, {n + 1}]]; (* _Jean-François Alcover_, Mar 27 2013, after A005187 *)
%Y A187791 Cf. A003506.
%K A187791 nonn,frac,less
%O A187791 0,2
%A A187791 _Paul Curtz_, Jan 06 2013
%E A187791 New definition by _M. F. Hasler_