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 A277457 #13 Nov 08 2017 02:30:58
%S A277457 1,3,12,71,616,7197,105052,1829291,36922928,846851993,21744781684,
%T A277457 617832652527,19242299657896,651815827343189,23857403245171724,
%U A277457 938247816632341043,39455261828928309088,1766645684585351990961,83913998998426051745764,4214295288128637488870327,223120214856875472660345176
%N A277457 E.g.f.: exp(2*x)/(1+LambertW(-x)).
%H A277457 G. C. Greubel, <a href="/A277457/b277457.txt">Table of n, a(n) for n = 0..385</a>
%F A277457 a(n) ~ exp(2*exp(-1)) * n^n.
%t A277457 CoefficientList[Series[Exp[2*x]/(1+LambertW[-x]), {x, 0, 20}], x]*Range[0, 20]!
%t A277457 Table[1 + Sum[Binomial[n, m]*(1 + Sum[Binomial[m, k]*k^k, {k, 1, m}]), {m, 1, n}], {n, 0, 20}]
%t A277457 Table[2^n + Sum[Binomial[n, k]*2^(n-k)*k^k, {k, 1, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Oct 28 2016 *)
%o A277457 (PARI) x='x+O('x^50); Vec(serlaplace(exp(2*x)/(1 + lambertw(-x)))) \\ _G. C. Greubel_, Nov 07 2017
%Y A277457 Cf. A086331, A277454, A277456, A277485.
%K A277457 nonn
%O A277457 0,2
%A A277457 _Vaclav Kotesovec_, Oct 16 2016