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