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Search: id:A121629
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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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+0
4
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| 1, 3, 16, 121, 1179, 14026, 196783, 3177861, 58019356, 1181098459, 26515026561, 650572403218, 17316566815441, 496889918749251, 15288155067806104, 502024850361876481, 17522822345606176083
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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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
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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
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Cf. A002720, A121630, A121631.
Sequence in context: A166883 A145158 A132070 this_sequence A141625 A053588 A035352
Adjacent sequences: A121626 A121627 A121628 this_sequence A121630 A121631 A121632
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KEYWORD
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nonn
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AUTHOR
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Karol A. Penson (penson(AT)lptl.jussieu.fr), Aug 12 2006
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