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 A353549 #18 Jul 23 2025 09:07:20
%S A353549 0,1,-1,12,-104,1289,-19605,356488,-7541464,182009385,-4935863537,
%T A353549 148600324124,-4918093868688,177482897072545,-6936155749635541,
%U A353549 291836667412104072,-13152940374866178512,632196357654491385521,-32280617841842744380161
%N A353549 Expansion of e.g.f. log(1+3*x) * exp(x)/3.
%F A353549 a(n) = n! * Sum_{k=0..n-1} (-3)^(n-1-k) / ((n-k) * k!).
%F A353549 a(0) = 0, a(1) = 1, a(n) = (-3 * n + 4) * a(n-1) + 3 * (n-1) * a(n-2) + 1.
%F A353549 a(n) ~ -(-1)^n * (n-1)! * 3^(n-1) / exp(1/3). - _Vaclav Kotesovec_, Jun 08 2022
%o A353549 (PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(log(1+3*x)*exp(x)/3)))
%o A353549 (PARI) a(n) = n!*sum(k=0, n-1, (-3)^(n-1-k)/((n-k)*k!));
%o A353549 (PARI) a_vector(n) = my(v=vector(n+1, i, if(i==2, 1, 0))); for(i=2, n, v[i+1]=(-3*i+4)*v[i]+3*(i-1)*v[i-1]+1); v;
%Y A353549 Cf. A002104, A353546, A353547, A353548, A354419.
%Y A353549 Cf. A346398.
%K A353549 sign
%O A353549 0,4
%A A353549 _Seiichi Manyama_, May 27 2022