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Search: id:A094072
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| A094072 |
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Coefficients arising in combinatorial field theory. |
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+0
1
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| 1, 6, 50, 615, 10192, 214571, 5544394, 171367020, 6208928376, 259542887975, 12356823485580, 662921411131909, 39714830070598204, 2636484537372437498, 192653800829700013970, 15405383160836582657251
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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P. Blasiak, K. A. Penson, A. I. Solomon, A. Horzela and G. E. H. Duchamp, Some useful combinatorial formulas for bosonic operators, J. Math. Phys. 46, 052110 (2005) (6 pages).
P. Blasiak, K. A. Penson, A. I. Solomon, A. Horzela and G E. H. Duchamp, Combinatorial field theories via boson normal ordering, preprint, Apr 27 2004.
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LINKS
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P. Blasiak, K. A. Penson, A. I. Solomon, A. Horzela and G. E. H. Duchamp, Combinatorial field theories via boson normal ordering
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FORMULA
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a(n)=B(n+1)*sum(binom(n+1, k)*k^(n+1-k), k=1..n+1), where B(n) are the Bell numbers (A000110). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 23 2004
E.g.f: exp(-1)*sum(exp(k*x*exp(k*x))/k!,k=0..infinity). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 26 2006
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MAPLE
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with(combinat): seq(bell(n+1)*sum(k^(n+1-k)*binomial(n+1, k), k=1..n+1), n=0..18);
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CROSSREFS
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Cf. A000085, A005425, A094065-.
Cf. A000110.
Adjacent sequences: A094069 A094070 A094071 this_sequence A094073 A094074 A094075
Sequence in context: A125558 A005416 A105617 this_sequence A058784 A008380 A066303
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KEYWORD
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nonn
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AUTHOR
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njas, May 01 2004
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 23 2004
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