Search: id:A005119
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%I A005119 M3024
%S A005119 1,1,3,16,124,1256,15576,226248,3729216,68179968,1361836800,29501349120,
%T A005119 693638208000,17815908096000,502048890201600,15388268595840000,
%U A005119 500579319427891200,16817771937344716800,581609175119297740800
%N A005119 Infinitesimal generator of x(x+1).
%D A005119 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005119 G. Labelle, Sur l'inversion et l'iteration continue des series formelles, 
               Europ. J. Combin., 1 (1980), 113-138.
%F A005119 a(n) = (n-2)!*Sum_{i=1..n-1} (-1)^(i+1)*C(n-i+1,i+1)*a(n-i)/(n-i-1)! 
               for n>1 with a(1)=1. E.g.f. satisfies: A(x) = (1-x)^2/(1-2x)*A(x-x^2) 
               where A(x) = Sum_{n>=0}a(n+1)*x^n/n! with offset so that A(0)=1. 
               - Paul D. Hanna (pauldhanna(AT)juno.com), Dec 27 2007
%o A005119 (PARI) {a(n)=if(n<1,0,if(n==1,1,(n-2)!*sum(i=1,n-1,(-1)^(i+1)*binomial(n-i+1,
               i+1)*a(n-i)/(n-i-1)!)))} - Paul D. Hanna (pauldhanna(AT)juno.com), 
               Dec 27 2007
%Y A005119 Sequence in context: A035352 A159607 A087018 this_sequence A090135 A157457 
               A000950
%Y A005119 Adjacent sequences: A005116 A005117 A005118 this_sequence A005120 A005121 
               A005122
%K A005119 nonn,nice
%O A005119 1,3
%A A005119 N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
%E A005119 More terms from Paul D. Hanna (pauldhanna(AT)juno.com), Dec 27 2007

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