A094072 Coefficients arising in combinatorial field theory.

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

Table of n, a(n) for n=0..15.

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, A094070, A094071, A094073, A094074.

Cf. A000110.

Sequence in context: A300989 A105617 A297926 * A361193 A363315 A058784

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