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 A337000 #7 Aug 09 2021 06:31:45
%S A337000 1,2,7,34,211,1596,14259,147106,1722683,22591408,328161643,5232410646,
%T A337000 90880495347,1708304787892,34557610000931,748647340991818,
%U A337000 17294012137850443,424368973372593432,11024176183963527099,302260934814635426014,8722906492537092723395
%N A337000 E.g.f.: 1 / ((1 - x)*(2 - exp(x))).
%C A337000 Exponential convolution of Fubini numbers (A000670) and factorial numbers (A000142).
%F A337000 a(n) = n! * Sum_{k=0..n} A000670(k) / k!.
%F A337000 a(0) = 1; a(n) = 2 * n * a(n-1) - Sum_{k=2..n} binomial(n,k) * (k-1) * a(n-k).
%F A337000 a(n) ~ n! / (2 * (1 - log(2)) * log(2)^(n+1)). - _Vaclav Kotesovec_, Aug 09 2021
%t A337000 nmax = 20; CoefficientList[Series[1/((1 - x) (2 - Exp[x])), {x, 0, nmax}], x] Range[0, nmax]!
%t A337000 Table[n! Sum[HurwitzLerchPhi[1/2, -k, 0]/(2 k!), {k, 0, n}], {n, 0, 20}]
%t A337000 a[0] = 1; a[n_] := a[n] = 2 n a[n - 1] - Sum[Binomial[n, k] (k - 1) a[n - k], {k, 2, n}]; Table[a[n], {n, 0, 20}]
%Y A337000 Cf. A000142, A000670, A101053.
%K A337000 nonn
%O A337000 0,2
%A A337000 _Ilya Gutkovskiy_, Aug 10 2020