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 A367940 #8 Dec 07 2023 08:23:25
%S A367940 1,1,17,113,1377,17185,252401,4104721,73500609,1430779713,30026750161,
%T A367940 674586467505,16130795165473,408560492670049,10915540174130353,
%U A367940 306531211899158609,9019774516570506113,277345675943850865281,8889954225208868308369,296408283056785166556401
%N A367940 Expansion of e.g.f. exp(exp(4*x) - 1 - 3*x).
%F A367940 G.f. A(x) satisfies: A(x) = 1 - x * ( 3 * A(x) - 4 * A(x/(1 - 4*x)) / (1 - 4*x) ).
%F A367940 a(n) = exp(-1) * Sum_{k>=0} (4*k-3)^n / k!.
%F A367940 a(0) = 1; a(n) = -3 * a(n-1) + Sum_{k=1..n} binomial(n-1,k-1) * 4^k * a(n-k).
%F A367940 a(n) = Sum_{k=0..n} binomial(n,k) * (-3)^(n-k) * 4^k * Bell(k).
%t A367940 nmax = 19; CoefficientList[Series[Exp[Exp[4 x] - 1 - 3 x], {x, 0, nmax}], x] Range[0, nmax]!
%t A367940 a[0] = 1; a[n_] := a[n] = -3 a[n - 1] + Sum[Binomial[n - 1, k - 1] 4^k a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]
%t A367940 Table[Sum[Binomial[n, k] (-3)^(n - k) 4^k BellB[k], {k, 0, n}], {n, 0, 19}]
%o A367940 (PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(exp(4*x) - 1 - 3*x))) \\ _Michel Marcus_, Dec 07 2023
%Y A367940 Cf. A000110, A124311, A355163, A346738, A367786, A367939.
%K A367940 nonn
%O A367940 0,3
%A A367940 _Ilya Gutkovskiy_, Dec 05 2023