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A032033
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Stirling transform of A032031.
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4
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1, 3, 21, 219, 3045, 52923, 1103781, 26857659, 746870565, 23365498683, 812198635941, 31055758599099, 1295419975298085, 58538439796931643, 2848763394161128101, 148537065755389540539, 8261178848690959117605
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Also "AIJ" (ordered, indistinct, labeled) transform of 3,3,3,3...
Third row of array A094416 (generalized ordered Bell numbers).
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LINKS
| C. G. Bower, Transforms (2)
P. Blasiak, K. A. Penson and A. I. Solomon, Dobinski-type relations and the log-normal distribution, arXiv:quant-ph/0303030, J. Phys. A.: Math. Gen 36 (2003) L273.
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FORMULA
| E.g.f.: 1/(4-3*e^x).
a(n) = 3*A050352(n), n>0.
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]
G.f. A(x)=B(x)/x, where B(x)=x+3*x^2+21*x^3+... =sum_{n>=1} b(n)*x^n satisfies 4*B(x)-x = 3*B(x/(1-x)), and b(n)=3*sum(k..1,n-1, binomial(n-1,k-1)*b(k)), b(1)=1. [From Vladimir Kruchinin, Jan 27 2011]
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MATHEMATICA
| a[n_] := PolyLog[-n, 3/4]/4; a[0] = 1; Table[a[n], {n, 0, 16}] (* From Jean-François Alcover, Nov 14 2011 *)
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CROSSREFS
| Cf. A032031.
Sequence in context: A168479 A158838 A107716 * A099121 A107864 A113663
Adjacent sequences: A032030 A032031 A032032 * A032034 A032035 A032036
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KEYWORD
| nonn,easy
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net)
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