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A121629
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Finite sum involving signless Stirling numbers of the first kind and the Bell numbers. Appears in the process of normal ordering of n-th power of (a)^2*(a+*a), where a+ and a are boson creation and annihilation operators, respectively.
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3
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1, 3, 16, 121, 1179, 14026, 196783, 3177861, 58019356, 1181098459, 26515026561, 650572403218, 17316566815441, 496889918749251, 15288155067806104, 502024850361876481, 17522822345606176083
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| K. A. Penson, P. Blasiak, A. Horzela, G. H. E. Duchamp and A. I. Solomon, Laguerre-type derivatives: Dobinski relations and combinatorial identities, J. Math. Phys. vol. 50, 083512 (2009)
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FORMULA
| a(n)=sum(abs(stirling1(n+1,p))*2^(n-p+1)*bell(p-1),p=1..n+1), n=0,1...
E.g.f.: exp(((1-2*x)^(-1/2))-1)/(1-2*x). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 13 2006
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CROSSREFS
| Cf. A002720, A121630, A121631.
Sequence in context: A166883 A145158 A132070 * A200793 A141625 A053588
Adjacent sequences: A121626 A121627 A121628 * A121630 A121631 A121632
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KEYWORD
| nonn
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AUTHOR
| Karol A. Penson (penson(AT)lptl.jussieu.fr), Aug 12 2006
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