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 A129683 #11 Jan 19 2020 09:28:07
%S A129683 1,4,28,272,3344,49472,852928,16758016,369082624,8996922368,
%T A129683 240294124544,6974172532736,218457925292032,7342688736329728,
%U A129683 263513011737051136,10054112734940561408,406301504472849907712,17333090863574658842624,778298003006760943353856
%N A129683 Expansion of (1/(1-2x))*exp(2x/(1-2x)).
%C A129683 a(n) = 2^n*A002720(n).
%F A129683 E.g.f.: (1/(1-2x))*exp(2x/(1-2x)). - corrected by _Vaclav Kotesovec_, Sep 26 2013
%F A129683 a(n) = 2^n*n!*sum{k=0..n, C(n,k)/k!}.
%F A129683 Conjecture: a(n) -4*n*a(n-1) +4*(n-1)^2*a(n-2)=0. - _R. J. Mathar_, Nov 14 2011
%F A129683 a(n) ~ 2^(n-1/2)*n^(n+1/4)*exp(2*sqrt(n)-n-1/2) * (1 + 31/(48*sqrt(n))). - _Vaclav Kotesovec_, Sep 26 2013
%F A129683 a(n) = 2^n*n!*LaguerreL(n, -1). - _Peter Luschny_, Jan 19 2020
%p A129683 a := n -> 2^n*n!*LaguerreL(n, -1):
%p A129683 seq(simplify(a(n)), n=0..18); # _Peter Luschny_, Jan 19 2020
%t A129683 Table[2^n*n!*Sum[Binomial[n,k]/k!,{k,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Sep 26 2013 *)
%t A129683 CoefficientList[Series[(1/(1-2*x))*E^(2*x/(1-2*x)), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Sep 26 2013 *)
%K A129683 easy,nonn
%O A129683 0,2
%A A129683 _Paul Barry_, Apr 28 2007
%E A129683 Error in definition corrected by _Vaclav Kotesovec_, Sep 26 2013