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 A010743 #25 Mar 08 2023 03:53:59
%S A010743 1,2,4,8,1,1,1,1,-14,45,-101,189,-331,668,-1932,7206,-27779,101365,
%T A010743 -347439,1139851,-3690766,12258863,-43341845,166059261,-682516519,
%U A010743 2930522990,-12823188092,56366526324,-247898684759,1094571175769,-4890163717903,22310147976797
%N A010743 Shifts 4 places left under inverse binomial transform.
%H A010743 Alois P. Heinz, <a href="/A010743/b010743.txt">Table of n, a(n) for n = 0..740</a>
%H A010743 M. Bernstein and N. J. A. Sloane, <a href="https://arxiv.org/abs/math/0205301">Some canonical sequences of integers</a>, arXiv:math/0205301 [math.CO], 2002; Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
%H A010743 M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
%H A010743 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A010743 G.f. A(x) satisfies: A(x) = 1 + 2*x + 4*x^2 + 8*x^3 + x^4*A(x/(1 + x))/(1 + x). - _Ilya Gutkovskiy_, Feb 02 2022
%p A010743 a:= proc(n) option remember; (m-> `if`(m<0, 2^n,
%p A010743 add(a(m-j)*binomial(m, j)*(-1)^j, j=0..m)))(n-4)
%p A010743 end:
%p A010743 seq(a(n), n=0..35); # _Alois P. Heinz_, Feb 02 2022
%t A010743 a[n_] := a[n] = Function[m, If[m < 0, 2^n, Sum[a[m - j]* Binomial[m, j]*(-1)^j, {j, 0, m}]]][n - 4];
%t A010743 Table[a[n], {n, 0, 35}] (* _Jean-François Alcover_, Mar 08 2023, after _Alois P. Heinz_ *)
%Y A010743 Cf. A010739, A010741, A010745, A010747.
%K A010743 sign
%O A010743 0,2
%A A010743 _N. J. A. Sloane_, _Jonas Wallgren_