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 A367919 #6 Dec 05 2023 04:27:38
%S A367919 1,3,13,67,397,2627,19085,150339,1272205,11481155,109852813,
%T A367919 1109011779,11765211021,130707706435,1516160466573,18314760232771,
%U A367919 229865470694797,2991427959247939,40292570823959693,560791503840522563,8053114165521427341,119158887402348541507
%N A367919 Expansion of e.g.f. exp(4*(exp(x) - 1) - x).
%F A367919 G.f. A(x) satisfies: A(x) = 1 - x * ( A(x) - 4 * A(x/(1 - x)) / (1 - x) ).
%F A367919 a(n) = exp(-4) * Sum_{k>=0} 4^k * (k-1)^n / k!.
%F A367919 a(0) = 1; a(n) = -a(n-1) + 4 * Sum_{k=1..n} binomial(n-1,k-1) * a(n-k).
%t A367919 nmax = 21; CoefficientList[Series[Exp[4 (Exp[x] - 1) - x], {x, 0, nmax}], x] Range[0, nmax]!
%t A367919 a[0] = 1; a[n_] := a[n] = -a[n - 1] + 4 Sum[Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 21}]
%Y A367919 Cf. A000296, A078944, A217924, A355254, A367891, A367920, A367921.
%K A367919 nonn
%O A367919 0,2
%A A367919 _Ilya Gutkovskiy_, Dec 04 2023