Search: id:A032033
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%I A032033
%S A032033 1,3,21,219,3045,52923,1103781,26857659,746870565,23365498683,
%T A032033 812198635941,31055758599099,1295419975298085,58538439796931643,
%U A032033 2848763394161128101,148537065755389540539,8261178848690959117605
%N A032033 Stirling transform of A032031.
%C A032033 Also "AIJ" (ordered, indistinct, labeled) transform of 3,3,3,3...
%C A032033 Generalized ordered Bell numbers Bo(3,n). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 03 2008]
%H A032033 C. G. Bower, <a href="transforms2.html">Transforms (2)</a>
%H A032033 P. Blasiak, K. A. Penson and A. I. Solomon, <a href="http://arXiv.org/
               abs/quant-ph/0303030">Dobinski-type relations and the log-normal 
               distribution</a>.
%F A032033 E.g.f.: 1/(4-3*e^x).
%F A032033 a(n)=sum(stirling2(n, k)*(3^k)*k!, k=0..n).
%F A032033 a(n)=sum(k^n*(3/4)^k, k=0..infinity)/4. - Karol A. Penson (penson(AT)lptl.jussieu.fr), 
               Jan 25 2002
%F A032033 a(n)=Sum_{k, 0<=k<=n} A131689(n,k)*3^k. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 03 2008]
%Y A032033 Cf. A032031.
%Y A032033 Third row of array A094416 (generalized ordered Bell numbers).
%Y A032033 Equals 3 * A050352(n) for n>0.
%Y A032033 Sequence in context: A120972 A158838 A107716 this_sequence A099121 A107864 
               A113663
%Y A032033 Adjacent sequences: A032030 A032031 A032032 this_sequence A032034 A032035 
               A032036
%K A032033 nonn,easy
%O A032033 0,2
%A A032033 Christian G. Bower (bowerc(AT)usa.net)

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