%I A052813
%S A052813 1,1,4,27,260,3280,51414,965762,21175496,531317520,15021531840,
%T A052813 472654558992,16385500397496,620612495460048,25500923655523848,
%U A052813 1129909190812470840,53705490284841870144,2725878142900911376896
%N A052813 A simple grammar.
%C A052813 E.g.f. of A052807 equals log(A(x)) = -log(1-x)*A(x). - Paul D. Hanna 
               (pauldhanna(AT)juno.com), Jul 19 2006
%H A052813 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=778">
               Encyclopedia of Combinatorial Structures 778</a>
%F A052813 E.g.f.: -1/ln(-1/(-1+x))*LambertW(-ln(-1/(-1+x)))
%F A052813 a(n) = Sum_{k=0..n} |Stirling1(n, k)|*(k+1)^(k-1). - Vladeta Jovovic 
               (vladeta(AT)eunet.rs), Nov 12 2003
%F A052813 E.g.f. satisfies: A(x) = 1/(1-x)^A(x). - Paul D. Hanna (pauldhanna(AT)juno.com), 
               Jul 19 2006
%F A052813 E.g.f.: Sum_{n>=0} (n+1)^(n-1)*(-log(1-x))^n/n!. [From Paul D. Hanna 
               (pauldhanna(AT)juno.com), Jun 22 2009]
%e A052813 E.g.f.: A(x) = 1 + x + 4*x^2/2! + 27*x^3/3! + 260*x^4/4! +...
%e A052813 Log(A(x))/A(x) = -log(1-x) = x + 1/2*x^2 + 1/3*x^3 + 1/4*x^4 +...
%p A052813 spec := [S,{C=Cycle(Z),S=Set(B),B=Prod(C,S)},labeled]: seq(combstruct[count](spec,
               size=n), n=0..20);
%o A052813 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1/(1-x+x*O(x^n))^A);n!*polcoeff(A,
               n)} - Paul D. Hanna (pauldhanna(AT)juno.com), Jul 19 2006
%o A052813 (PARI) {a(n)=n!*polcoeff(sum(m=0,n,(m+1)^(m-1)/m!*(-log(1-x+x*O(x^n)))^m),
               n)} [From Paul D. Hanna (pauldhanna(AT)juno.com), Jun 22 2009]
%Y A052813 Cf. A052807 (log(A(x)).
%Y A052813 Sequence in context: A070271 A000312 A050764 this_sequence A121353 A161633 
               A052871
%Y A052813 Adjacent sequences: A052810 A052811 A052812 this_sequence A052814 A052815 
               A052816
%K A052813 easy,nonn
%O A052813 0,3
%A A052813 encyclopedia(AT)pommard.inria.fr, Jan 25 2000