A094070 a(n) = A000085(n) * A000110(n).

1, 4, 20, 150, 1352, 15428, 203464, 3162960, 55405140, 1101298600, 24222234720, 590544046744, 15715973012248, 456341011254560, 14312979247985120, 484253161428902192, 17550722413456774848, 680244627812139042016, 28053748582811428182080, 1228896901162555453603712

Offset: 0

Author

N. J. A. Sloane, May 01 2004

Keywords

• nonn

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, arXiv:quant-ph/0405103, 2004-2006. The title of this paper in the arXiv was later changed to "Some useful combinatorial formulas for bosonic operators"
• A. Horzela, P. Blasiak, G. E. H. Duchamp, K. A. Penson and A. I. Solomon, A product formula and combinatorial field theory

Crossrefs

Cf. A000085, A005425, A094071, A094072, A094073, A094074.

Programs

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 *)

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

Extensions

More terms from Ralf Stephan, Oct 14 2004