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A094072
Coefficients arising in combinatorial field theory.
4
1, 6, 50, 615, 10192, 214571, 5544394, 171367020, 6208928376, 259542887975, 12356823485580, 662921411131909, 39714830070598204, 2636484537372437498, 192653800829700013970, 15405383160836582657251
OFFSET
0,2
REFERENCES
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).
LINKS
P. Blasiak, K. A. Penson, A. I. Solomon, A. Horzela and G. E. H. Duchamp, Combinatorial field theories via boson normal ordering, arXiv:quant-ph/0405103, 2004-2006.
FORMULA
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
MAPLE
with(combinat): seq(bell(n+1)*sum(k^(n+1-k)*binomial(n+1, k), k=1..n+1), n=0..18);
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 01 2004
EXTENSIONS
More terms from Emeric Deutsch, Nov 23 2004
STATUS
approved