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 A195005 #27 Oct 10 2020 12:12:56
%S A195005 1,2,34,1490,122530,16227602,3155309794,846406200530,299510392317730,
%T A195005 135163342884412562,75760096553546176354,51633670624622762956370,
%U A195005 42049600429338786951232930,40326932840083815683430101522,44984263429111569097120217311714
%N A195005 E.g.f.: Sum_{n>=0} 2^n*(exp(n*x) - 1)^n.
%H A195005 Vaclav Kotesovec, <a href="/A195005/b195005.txt">Table of n, a(n) for n = 0..217</a>
%F A195005 a(n) = Sum_{k=0..n} 2^k*k^n*k!*Stirling2(n,k).
%F A195005 a(n) ~ c * (1 + 2*exp(1/r))^n * r^(2*n) * n!^2 / sqrt(n), where r = 0.925556278640887084941460444526398190071550948416... is the root of the equation exp(1/r) * (1 + 1/(r*LambertW(-exp(-1/r)/r))) = -1/2 and c = 0.3559088366632706316517829481255877447669425726507348... - _Vaclav Kotesovec_, Oct 04 2020
%e A195005 E.g.f.: A(x) = 1 + 2*x + 34*x^2/2! + 1490*x^3/3! + 122530*x^4/4! +...
%e A195005 where
%e A195005 A(x) = 1 + 2*(exp(x)-1) + 2^2*(exp(2*x)-1)^2 + 2^3*(exp(3*x)-1)^3 +...
%t A195005 Flatten[{1, Table[Sum[2^k * k^n * k! * StirlingS2[n,k], {k,0,n}], {n,1,20}]}] (* _Vaclav Kotesovec_, Oct 04 2020 *)
%o A195005 (PARI) {a(n)=local(X=x+x*O(x^n));n!*polcoeff(sum(m=0,n,2^m*(exp(m*X)-1)^m),n)}
%o A195005 (PARI) {Stirling2(n, k)=if(k<0|k>n, 0, sum(i=0, k, (-1)^i*binomial(k, i)/k!*(k-i)^n))}
%o A195005 {a(n)=sum(k=0, n, 2^k*k^n*k!*Stirling2(n, k))}
%Y A195005 Cf. A195263, A122399, A301581, A338040, A338044.
%K A195005 nonn
%O A195005 0,2
%A A195005 _Paul D. Hanna_, Sep 13 2011