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Search: id:A071379
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| A071379 |
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a(n)=sum(((k+4)!/k!)^(n-1)/k!,k=0..infinity)/exp(1),n=1,2... . This is a Dobinski-type summation formula. |
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5
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| 1, 209, 163121, 326922081, 1346634725665, 9939316337679281, 119802044788535500753, 2205421644124274191535553, 58945667435045762187763602753, 2198513228897522394476415669503377
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OFFSET
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1,2
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COMMENT
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a(n) quickly become gigantic: a(15)= 9142140479823239889945170786704021785456107245847570873873. a(n) appears in the process of ordering the n-th power of a product of fourth power of boson creation and fourth power of boson annihilation operators.
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REFERENCES
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P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem, Phys. Lett. A 309 (2003) 198-205.
M. Schork, On the combinatorics of normal ordering bosonic operators and deforming it, J. Phys. A 36 (2003) 4651-4665.
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LINKS
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P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem.
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FORMULA
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sum((fallfac(k, 4)^n)/k!, k=4..infinity)/exp(1), n>=1, with fallfac(n, m) := A08279(n, m) (falling factorials). (From eq.(26) with r=4 of the Schork reference.)
E.g.f. with a(0) := 1: (sum((exp(fallfac(k, 4)*x))/k!, k=4..infinity)+8/3)/exp(1). From top of p. 4656 with r=4 of the Schork reference.
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CROSSREFS
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Cf. A000110, A020556 and A069223, when k+4 is replaced by k+1, k+2 or k+3 respectively.
Sequence in context: A157441 A029554 A003779 this_sequence A125549 A104876 A050516
Adjacent sequences: A071376 A071377 A071378 this_sequence A071380 A071381 A071382
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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), May 22 2002
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