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 A052858 #22 Jan 22 2025 06:38:53
%S A052858 0,0,2,3,16,65,456,3157,28624,276705,3136240,38531141,528468744,
%T A052858 7837577761,126588882616,2194957583925,40854219413536,810192673705793,
%U A052858 17082845929433952,381225135102420997
%N A052858 Expansion of e.g.f. log(-1/(-1+x*exp(x)-x)).
%C A052858 Previous name was: A simple grammar.
%H A052858 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=826">Encyclopedia of Combinatorial Structures 826</a>
%F A052858 E.g.f.: log(-1/(-1+x*exp(x)-x))
%F A052858 a(n) ~ (n-1)! * r^n, where r = 1.23997788765655... is the root of the equation log(1+r)=1/r. - _Vaclav Kotesovec_, Sep 29 2013
%F A052858 a(n) = n!*Sum_{k=1..n/2}((k-1)!*stirling2(n-k,k)/(n-k)!). - _Vladimir Kruchinin_, Mar 22 2016
%F A052858 a(0) = a(1) = 0; a(n) = n + Sum_{k=2..n-1} k * binomial(n-1,k) * a(n-k). - _Seiichi Manyama_, Jan 21 2025
%p A052858 spec := [S,{B=Set(Z,1 <= card),C=Prod(Z,B),S=Cycle(C)},labeled]: seq(combstruct[count](spec, size=n), n=0..20);
%t A052858 CoefficientList[Series[Log[-1/(-1+x*E^x-x)], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Sep 29 2013 *)
%o A052858 (Maxima)
%o A052858 a(n):=(n)!*sum((k-1)!*stirling2(n-k,k)/(n-k)!,k,1,n/2); /* _Vladimir Kruchinin_, Mar 22 2016 */
%K A052858 easy,nonn
%O A052858 0,3
%A A052858 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052858 New name using e.g.f. by _Joerg Arndt_, Sep 30 2013