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 A337010 #5 Aug 11 2020 19:47:56
%S A337010 1,4,18,92,532,3440,24552,191280,1612304,14597952,141123872,
%T A337010 1449324992,15743376704,180203389696,2166381979264,27274611880704,
%U A337010 358690234163456,4916123783848960,70076765972288000,1036967662211324928,15902394743591408640
%N A337010 a(n) = exp(-1/2) * Sum_{k>=0} (2*k + 3)^n / (2^k * k!).
%F A337010 E.g.f.: exp(3*x + (exp(2*x) - 1) / 2).
%F A337010 a(0) = 1; a(n) = 4 * a(n-1) + Sum_{k=2..n} binomial(n-1,k-1) * 2^(k-1) * a(n-k).
%F A337010 a(n) = Sum_{k=0..n} binomial(n,k) * A004211(k+1).
%F A337010 a(n) = Sum_{k=0..n} binomial(n,k) * 3^(n-k) * A004211(k).
%t A337010 nmax = 20; CoefficientList[Series[Exp[3 x + (Exp[2 x] - 1)/2], {x, 0, nmax}], x] Range[0, nmax]!
%t A337010 a[0] = 1; a[n_] := a[n] = 4 a[n - 1] + Sum[Binomial[n - 1, k - 1] 2^(k - 1) a[n - k], {k, 2, n}]; Table[a[n], {n, 0, 20}]
%Y A337010 Cf. A004211, A005494, A007405, A337011.
%K A337010 nonn
%O A337010 0,2
%A A337010 _Ilya Gutkovskiy_, Aug 11 2020