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 A100735 #18 Feb 18 2020 01:16:42
%S A100735 1,1,3,3,15,15,45,45,255,255,765,765,3825,3825,11475,11475,65535,
%T A100735 65535,196605,196605,983025,983025,2949075,2949075,16711425,16711425,
%U A100735 50134275,50134275,250671375,250671375,752014125,752014125,4294967295,4294967295
%N A100735 Inverse modulo 2 binomial transform of 2^n.
%C A100735 The modulo 2 binomial transform and its inverse are defined by
%C A100735 B(n) = Sum_{k=0..n} (binomial(n,k) mod 2)*A(k),
%C A100735 A(n) = Sum_{k=0..n} (-1)^A010060(n-k)*(binomial(n, k) mod 2)*B(k). - _N. J. A. Sloane_, Dec 20 2019
%C A100735 2^n may be retrieved as Sum_{k=0..n} mod(binomial(n,k),2)*a(k).
%H A100735 G. C. Greubel, <a href="/A100735/b100735.txt">Table of n, a(n) for n = 0..1000</a>
%H A100735 Thomas Baruchel, <a href="https://arxiv.org/abs/1912.00452">A non-symmetric divide-and-conquer recursive formula for the convolution of polynomials and power series</a>, arXiv:1912.00452 [math.NT], 2019.
%F A100735 a(n) = Sum_{k=0..n} (-1)^A010060(n-k)*mod(binomial(n, k), 2)*2^k.
%t A100735 Table[Sum[(-1)^ThueMorse[n - k]*Mod[Binomial[n, k], 2]*2^k, {k, 0, n}], {n, 0, 50}] (* _G. C. Greubel_, Apr 17 2018 *)
%o A100735 (PARI) for(n=0,50, print1(abs(sum(k=0,n,(-1)^(hammingweight(k)%2)* lift(Mod(binomial(n,k),2))*2^k)), ", ")) \\ _G. C. Greubel_, Apr 17 2018
%Y A100735 Cf. A047999, A166282.
%K A100735 easy,nonn
%O A100735 0,3
%A A100735 _Paul Barry_, Dec 06 2004