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 A354419 #21 Jul 23 2025 09:07:15
%S A354419 0,1,-2,23,-276,4509,-91190,2205587,-62104168,1995807993,-72089029802,
%T A354419 2891304481999,-127498010037244,6131189086886421,-319320539953144158,
%U A354419 17905976286288568267,-1075611833288214177232,68909527979479961534705
%N A354419 Expansion of e.g.f. log(1+4*x) * exp(x)/4.
%F A354419 a(n) = n! * Sum_{k=0..n-1} (-4)^(n-1-k) / ((n-k) * k!).
%F A354419 a(0) = 0, a(1) = 1, a(n) = (-4 * n + 5) * a(n-1) + 4 * (n-1) * a(n-2) + 1.
%F A354419 a(n) ~ -(-1)^n * (n-1)! * 4^(n-1) / exp(1/4). - _Vaclav Kotesovec_, Jun 08 2022
%o A354419 (PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(log(1+4*x)*exp(x)/4)))
%o A354419 (PARI) a(n) = n!*sum(k=0, n-1, (-4)^(n-1-k)/((n-k)*k!));
%o A354419 (PARI) a_vector(n) = my(v=vector(n+1, i, if(i==2, 1, 0))); for(i=2, n, v[i+1]=(-4*i+5)*v[i]+4*(i-1)*v[i-1]+1); v;
%Y A354419 Cf. A002104, A353546, A353547, A353548, A353549.
%K A354419 sign
%O A354419 0,3
%A A354419 _Seiichi Manyama_, May 27 2022