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 A353546 #18 Jul 23 2025 09:07:33
%S A353546 0,1,4,17,96,729,7060,83033,1146656,18164625,324488068,6450956929,
%T A353546 141233271872,3376008830505,87480173354964,2442396780039817,
%U A353546 73089894980585408,2333809837398044321,79198287879591647364,2846319497398561356913
%N A353546 Expansion of e.g.f. -log(1-2*x) * exp(x)/2.
%F A353546 a(n) = n! * Sum_{k=0..n-1} 2^(n-1-k) / ((n-k) * k!).
%F A353546 a(0) = 0, a(1) = 1, a(n) = (2 * n - 1) * a(n-1) - 2 * (n-1) * a(n-2) + 1.
%F A353546 a(n) ~ (n-1)! * exp(1/2) * 2^(n-1). - _Vaclav Kotesovec_, Jun 08 2022
%o A353546 (PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-log(1-2*x)*exp(x)/2)))
%o A353546 (PARI) a(n) = n!*sum(k=0, n-1, 2^(n-1-k)/((n-k)*k!));
%o A353546 (PARI) a_vector(n) = my(v=vector(n+1, i, if(i==2, 1, 0))); for(i=2, n, v[i+1]=(2*i-1)*v[i]-2*(i-1)*v[i-1]+1); v;
%Y A353546 Cf. A002104, A353547, A353548, A353549.
%Y A353546 Cf. A346394.
%Y A353546 Essentially partial sums of A010844.
%K A353546 nonn
%O A353546 0,3
%A A353546 _Seiichi Manyama_, May 27 2022