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 A337011 #8 Aug 14 2020 12:13:29
%S A337011 1,5,27,159,1025,7221,55307,457631,4065569,38566021,388757083,
%T A337011 4146851583,46636281185,551163837685,6825500514059,88341860285631,
%U A337011 1192267628956353,16743728349797765,244221140242647579,3693367920926321375,57821628101627115329
%N A337011 a(n) = 2^n * exp(-1/2) * Sum_{k>=0} (k + 2)^n / (2^k * k!).
%H A337011 Robert Israel, <a href="/A337011/b337011.txt">Table of n, a(n) for n = 0..513</a>
%F A337011 E.g.f.: exp(4*x + (exp(2*x) - 1) / 2).
%F A337011 a(0) = 1; a(n) = 5 * a(n-1) + Sum_{k=2..n} binomial(n-1,k-1) * 2^(k-1) * a(n-k).
%F A337011 a(n) = Sum_{k=0..n} binomial(n,k) * 4^(n-k) * A004211(k).
%p A337011 E:= exp(4*x+exp(2*x)/2-1/2):
%p A337011 S:= series(E,x,31):
%p A337011 seq(coeff(S,x,n)*n!,n=0..30); # _Robert Israel_, Aug 14 2020
%t A337011 nmax = 20; CoefficientList[Series[Exp[4 x + (Exp[2 x] - 1)/2], {x, 0, nmax}], x] Range[0, nmax]!
%t A337011 a[0] = 1; a[n_] := a[n] = 5 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 A337011 Cf. A004211, A007405, A045379, A337010.
%K A337011 nonn
%O A337011 0,2
%A A337011 _Ilya Gutkovskiy_, Aug 11 2020