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 A347005 #7 Aug 10 2021 18:48:21
%S A347005 1,1,5,28,205,1856,19964,249005,3535613,56339884,996009280,
%T A347005 19350090365,409850078356,9400728524669,232154433941057,
%U A347005 6141705628777193,173295665869432733,5195039603196754564,164890990869273983108,5524278740902526776085,194815729875439415542760
%N A347005 E.g.f.: Product_{k>=1} 1 / (1 - exp(x) * x^k / k!).
%F A347005 E.g.f.: exp( Sum_{k>=1} ( Sum_{d|k} exp(d*x) / (d * ((k/d)!)^d) ) * x^k ).
%F A347005 E.g.f.: Product_{k>=1} 1 / (1 - Sum_{j>=k} binomial(j,k) * x^j / j!).
%F A347005 a(n) ~ c * n! / ((1 + LambertW(1)) * LambertW(1)^n), where c = Product_{k>=2} (1/(1 - LambertW(1)^(k-1)/k!)) = 1.487589725380080111479849424209442083... - _Vaclav Kotesovec_, Aug 10 2021
%t A347005 nmax = 20; CoefficientList[Series[Product[1/(1 - Exp[x] x^k/k!), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%Y A347005 Cf. A005651, A140585, A265953, A347006.
%K A347005 nonn
%O A347005 0,3
%A A347005 _Ilya Gutkovskiy_, Aug 10 2021