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 A010745 #25 Jan 13 2025 07:56:40
%S A010745 1,2,4,8,16,1,1,1,1,1,-30,124,-336,734,-1401,2404,-3485,2212,14630,
%T A010745 -105408,497131,-1995782,7265342,-24576128,77966104,-231218343,
%U A010745 626012198,-1430352680,1894959964,6114950887,-73791743479,472896657475,-2523776826105,12272646042530
%N A010745 Shifts 5 places left under inverse binomial transform.
%H A010745 Alois P. Heinz, <a href="/A010745/b010745.txt">Table of n, a(n) for n = 0..775</a>
%H A010745 M. Bernstein and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
%H A010745 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 A010745 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A010745 G.f. A(x) satisfies: A(x) = 1 + 2*x + 4*x^2 + 8*x^3 + 16*x^4 + x^5*A(x/(1 + x))/(1 + x). - _Ilya Gutkovskiy_, Feb 02 2022
%p A010745 a:= proc(n) option remember; (m-> `if`(m<0, 2^n,
%p A010745 add(a(m-j)*binomial(m, j)*(-1)^j, j=0..m)))(n-5)
%p A010745 end:
%p A010745 seq(a(n), n=0..35); # _Alois P. Heinz_, Feb 02 2022
%t A010745 a[n_] := a[n] = Function[m, If[m < 0, 2^n, Sum[a[m-j]*Binomial[m, j]*(-1)^j, {j, 0, m}]]][n-5]; Table[a[n], {n, 0, 35}] (* _Jean-François Alcover_, Jan 13 2025, after _Alois P. Heinz_ *)
%Y A010745 Cf. A010739, A010741, A010743, A010747.
%K A010745 sign
%O A010745 0,2
%A A010745 _N. J. A. Sloane_, _Jonas Wallgren_