Search: id:A052881
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%I A052881
%S A052881 0,0,2,9,44,250,1644,12348,104544,986256,10265760,116915040,
%T A052881 1446526080,19323757440,277238626560,4251984710400,69426608025600,
%U A052881 1202482800691200,22021300630425600,425162773111910400
%N A052881 A simple grammar.
%H A052881 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=853">
               Encyclopedia of Combinatorial Structures 853</a>
%F A052881 E.g.f.: -ln(-1/(-1+x))*x/(-1+x)
%F A052881 Recurrence: {a(1)=0, a(2)=2, (n^3+3*n^2+2*n)*a(n)+(-5*n-2*n^2-2)*a(n+1)+(n+1)*a(n+2)}
%F A052881 a(n) = n!*Sum 1/i, i = 1..(n-1) = s(n, 2)-(n-1)! = n*s(n-1, 2) = n*a(n-1) 
               + (n-1)! + (n-2)! = A000142(n)*A001008(n-1)/A002805(n-1) = A000254(n)-A000142(n-1) 
               = A000027(n)*A000254(n-1) = a(n-1)*A000027(n) + A001048(n-1). - Henry 
               Bottomley (se16(AT)btinternet.com), May 05 2001
%p A052881 spec := [S,{B=Sequence(Z,1 <= card),C=Cycle(Z),S=Prod(B,C)},labeled]: 
               seq(combstruct[count](spec,size=n), n=0..20);
%p A052881 with(combinat):a:=n->abs(stirling1(n,2))*n: seq(a(n), n=0..19); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Oct 05 2007
%o A052881 sage: [stirling_number1(i,2)*i for i in xrange(0,32)] - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jun 27 2008
%Y A052881 Sequence in context: A108308 A119855 A047119 this_sequence A020071 A000166 
               A093464
%Y A052881 Adjacent sequences: A052878 A052879 A052880 this_sequence A052882 A052883 
               A052884
%K A052881 easy,nonn
%O A052881 0,3
%A A052881 encyclopedia(AT)pommard.inria.fr, Jan 25 2000

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