A052865 - OEIS

%I #21 Jul 04 2018 08:56:41

%S 0,0,2,18,166,1720,20168,265776,3900048,63160944,1119902112,

%T 21588456912,449695165104,10068121989120,241142216363904,

%U 6153066311872128,166649425520796288,4775084999073669888,144324648624594398976,4589066547251186277888

%N E.g.f.: log(-1/(-1+x))^2 / (-1 + log(-1/(-1+x)))^2.

%C Previous name was: A simple grammar.

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=833">Encyclopedia of Combinatorial Structures 833</a>

%F E.g.f.: log(-1/(-1+x))^2 / (-1 + log(-1/(-1+x)))^2.

%F a(n) = sum(k=1..n, (k-1)*k!*(-1)^(n-k)*Stirling1(n,k)). - _Vladimir Kruchinin_, Sep 26 2011

%F a(n) ~ n! * exp(n)*n/(exp(1)-1)^(n+2). - _Vaclav Kotesovec_, Sep 29 2013

%p spec := [S,{C=Cycle(Z),B=Sequence(C,1 <= card),S=Prod(B,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

%t CoefficientList[Series[Log[-1/(-1+x)]^2/(-1+Log[-1/(-1+x)])^2, {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Sep 29 2013 *)

%o (Maxima) a(n):=sum((k-1)*k!*(-1)^(n-k)*stirling1(n,k),k,1,n); /* _Vladimir Kruchinin_, Sep 26 2011 */

%K easy,nonn

%O 0,3

%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000

%E New name using e.g.f., _Joerg Arndt_, Sep 30 2013