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 A072034 #46 Feb 20 2021 11:03:30
%S A072034 1,1,6,54,680,11000,217392,5076400,136761984,4175432064,142469423360,
%T A072034 5372711277824,221903307604992,9961821300640768,482982946946734080,
%U A072034 25150966159083264000,1400031335107317628928,82960293298087664648192
%N A072034 a(n) = Sum_{k=0..n} binomial(n,k)*k^n.
%C A072034 The number of functions from {1,2,...,n} into a subset of {1,2,...,n} summed over all subsets. - _Geoffrey Critzer_, Sep 16 2012
%H A072034 Vincenzo Librandi, <a href="/A072034/b072034.txt">Table of n, a(n) for n = 0..200</a>
%H A072034 V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Interesting asymptotic formulas for binomial sums</a>, Jun 09 2013
%F A072034 E.g.f.: 1/(1+LambertW(-x*exp(x))). - _Vladeta Jovovic_, Mar 29 2008
%F A072034 a(n) ~ (n/(e*LambertW(1/e)))^n/sqrt(1+LambertW(1/e)). - _Vaclav Kotesovec_, Nov 26 2012
%F A072034 O.g.f.: Sum_{n>=0} n^n * x^n / (1 - n*x)^(n+1). - _Paul D. Hanna_, May 22 2018
%p A072034 seq(add(binomial(n,k)*k^n,k=0..n),n=0..17); # _Peter Luschny_, Jun 09 2015
%t A072034 Table[Sum[Binomial[n,k]k^n,{k,0,n}],{n,1,20}] (* _Geoffrey Critzer_, Sep 16 2012 *)
%o A072034 (PARI) x='x+O('x^50); Vec(serlaplace(1/(1 + lambertw(-x*exp(x))))) \\ _G. C. Greubel_, Nov 10 2017
%o A072034 (PARI) a(n) = sum(k=0, n, binomial(n,k)*k^n); \\ _Michel Marcus_, Nov 10 2017
%Y A072034 Cf. A088789, A242446, A256016, A336828, A341815.
%K A072034 nonn
%O A072034 0,3
%A A072034 _Karol A. Penson_, Jun 07 2002
%E A072034 Offset set to 0 and a(0) = 1 prepended by _Peter Luschny_, Jun 09 2015
%E A072034 E.g.f. edited to include a(0)=1 by _Robert Israel_, Jun 09 2015