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 A242735 #19 Apr 27 2019 21:06:35
%S A242735 0,0,0,1,1,1,-3,-1,1,3,15,3,-1,3,15,-35,-5,1,-1,5,35,315,35,-5,3,-5,
%T A242735 35,315,-693,-63,7,-3,3,-7,63,693,3003,231,-21,7,-5,7,-21,231,3003,
%U A242735 -6435,-429,33,-9,5,-5,9,-33,429,6435
%N A242735 Array read by antidiagonals: form difference table of the sequence of rationals 0, 0 followed by A001803(n)/A046161(n), then extract numerators.
%C A242735 Difference table of c(n)/d(n) = 0, 0, followed by A001803(n)/A046161(n):
%C A242735 0, 0, 1, 3/2, 15/8, 35/16, 315/128, ...
%C A242735 0, 1, 1/2, 3/8, 5/16, 35/128, 63/256, ...
%C A242735 1, -1/2, -1/8, -1/16, -5/128, -7/256, -21/1024, ...
%C A242735 -3/2, 3/8, 1/16, 3/128, 3/256, 7/1024, 9/2048, ...
%C A242735 15/8, -5/16, -5/128, -3/256, -5/1024, -5/2048, -45/32768, ...
%C A242735 -35/16, 35/128, 7/256, 7/1024, 5/2048, 35/32768, 35/65536, ... etc.
%C A242735 d(n) = 1, 1, followed by A046161(n).
%C A242735 c(n)/d(n) is an autosequence (a sequence whose inverse binomial transform is the signed sequence) of the second kind (the main diagonal is equal to the first upper diagonal multiplied by 2). See A187791.
%C A242735 Antidiagonal denominators: repeat n+1 times d(n).
%C A242735 Second row without 0: Lorentz (gamma) factor = A001790(n)/A046161(n).
%C A242735 Third row: Lorentz beta factor = 1 followed by -A098597(n). Lorbeta(n) in A206771.
%e A242735 a(n) as a triangle:
%e A242735 0;
%e A242735 0, 0;
%e A242735 1, 1, 1;
%e A242735 -3, -1, 1, 3;
%e A242735 15, 3, -1, 3, 15;
%e A242735 etc.
%t A242735 c[n_] := (2*n-3)*Binomial[2*(n-2), n-2]/4^(n-2) // Numerator; d[n_] := Binomial[2*(n-2), n-2]/4^(n-2) // Denominator; Clear[a]; a[0, k_] := c[k]/d[k]; a[n_, k_] := a[n, k] = a[n-1, k+1] - a[n-1, k]; Table[a[n-k, k] // Numerator, {n, 0, 9}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Jun 17 2014 *)
%K A242735 sign,frac,tabl
%O A242735 0,7
%A A242735 _Paul Curtz_, May 21 2014