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A094072
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Coefficients arising in combinatorial field theory.
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4
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1, 6, 50, 615, 10192, 214571, 5544394, 171367020, 6208928376, 259542887975, 12356823485580, 662921411131909, 39714830070598204, 2636484537372437498, 192653800829700013970, 15405383160836582657251
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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).
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LINKS
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FORMULA
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a(n) = B(n+1)*Sum_{k=1..n+1} binomial(n+1, k)*k^(n+1-k), where B(n) are the Bell numbers (A000110). - Emeric Deutsch, Nov 23 2004
E.g.f.: exp(-1)*Sum_{k>=0} exp(k*x*exp(k*x))/k!. - Vladeta Jovovic, 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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MATHEMATICA
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Table[BellB[n+1]Sum[Binomial[n+1, k]k^(n+1-k), {k, n+1}], {n, 0, 20}] (* Harvey P. Dale, Feb 05 2015 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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