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 A127944 #12 Nov 15 2022 18:01:43
%S A127944 0,0,0,2,3,7,11,17,21,29,37,47,56,68,80,94,105,121,137,155,172,192,
%T A127944 212,234,254,278,302,328,353,381,409,439,465,497,529,563,596,632,668,
%U A127944 706,742,782,822,864,905,949,993,1039,1082,1130,1178,1228,1277
%N A127944 Partial sums of A093049.
%H A127944 G. C. Greubel, <a href="/A127944/b127944.txt">Table of n, a(n) for n = 0..10000</a>
%F A127944 a(n) = log_2(2^C(n+1,2)/denominator(C(2n,n)/4^n)).
%F A127944 a(n) = A000217(n) - A005187(n).
%F A127944 a(n) = log_2(A127943(n)).
%t A127944 Table[Log2[2^Binomial[n + 1, 2]/Denominator[Binomial[2 n, n]/4^n]], {n, 0, 100}] (* _G. C. Greubel_, May 01 2018 *)
%t A127944 Accumulate[Join[{0},Table[n-1-IntegerExponent[n,2],{n,80}]]] (* _Harvey P. Dale_, Nov 15 2022 *)
%o A127944 (Magma) [Floor(Log(2,(2^Binomial(n+1,2) / Denominator(Binomial(2*n,n) / 4^n)))): n in [0..80]]; // _Vincenzo Librandi_, May 02 2018
%K A127944 easy,nonn
%O A127944 0,4
%A A127944 _Paul Barry_, Feb 08 2007