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 A353548 #18 Jul 23 2025 09:07:24
%S A353548 0,1,6,47,540,8429,166210,3952955,109981816,3502905369,125648153278,
%T A353548 5011458069639,219987094389524,10538817637744005,547118005892177018,
%U A353548 30595552548140425747,1833501625083035349488,117219490267316310468913
%N A353548 Expansion of e.g.f. -log(1-4*x) * exp(x)/4.
%F A353548 a(n) = n! * Sum_{k=0..n-1} 4^(n-1-k) / ((n-k) * k!).
%F A353548 a(0) = 0, a(1) = 1, a(n) = (4 * n - 3) * a(n-1) - 4 * (n-1) * a(n-2) + 1.
%F A353548 a(n) ~ (n-1)! * exp(1/4) * 4^(n-1). - _Vaclav Kotesovec_, Jun 08 2022
%o A353548 (PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-log(1-4*x)*exp(x)/4)))
%o A353548 (PARI) a(n) = n!*sum(k=0, n-1, 4^(n-1-k)/((n-k)*k!));
%o A353548 (PARI) a_vector(n) = my(v=vector(n+1, i, if(i==2, 1, 0))); for(i=2, n, v[i+1]=(4*i-3)*v[i]-4*(i-1)*v[i-1]+1); v;
%Y A353548 Cf. A002104, A353546, A353547, A353549.
%Y A353548 Cf. A346396.
%Y A353548 Essentially partial sums of A056545.
%K A353548 nonn
%O A353548 0,3
%A A353548 _Seiichi Manyama_, May 27 2022