OFFSET
0,2
COMMENTS
Coefficients arising in combinatorial field theory.
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).
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.
LINKS
P. Blasiak, K. A. Penson, A. I. Solomon, A. Horzela and G. E. H. Duchamp, Combinatorial field theories via boson normal ordering
A. Horzela, P. Blasiak, G. E. H. Duchamp, K. A. Penson and A. I. Solomon, A product formula and combinatorial field theory
FORMULA
a(n) = (i/sqrt(2))^(n+1)*H(n+1, -i/sqrt(2))*Bell(n+1), where i=sqrt(-1), H(n, x) are the Hermite polynomials and Bell(n) are the Bell numbers. - Emeric Deutsch, Nov 22 2004
MAPLE
with(combinat): with(orthopoly): seq((I/sqrt(2))^(n+1)*H(n+1, -I/sqrt(2))*bell(n+1), n=0..17); # Emeric Deutsch, Nov 22 2004
MATHEMATICA
a[n_] := Sum[StirlingS1[n+1, k] 2^k BellB[k, 1/2], {k, 0, n+1}] BellB[n+1];
Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Aug 07 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 01 2004
EXTENSIONS
More terms from Ralf Stephan, Oct 14 2004
STATUS
approved