The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A094072 Coefficients arising in combinatorial field theory. 0
 1, 6, 50, 615, 10192, 214571, 5544394, 171367020, 6208928376, 259542887975, 12356823485580, 662921411131909, 39714830070598204, 2636484537372437498, 192653800829700013970, 15405383160836582657251 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A000085, A005425, A094065. Cf. A000110. Sequence in context: A300989 A105617 A297926 * A058784 A008380 A196905 Adjacent sequences:  A094069 A094070 A094071 * A094073 A094074 A094075 KEYWORD nonn AUTHOR N. J. A. Sloane, May 01 2004 EXTENSIONS More terms from Emeric Deutsch, Nov 23 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 20 19:29 EDT 2021. Contains 343137 sequences. (Running on oeis4.)