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

0,2

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

Table of n, a(n) for n=0..19.

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

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

Sequence in context: A001171 A247331 A167018 * A335627 A119022 A006682

Adjacent sequences: A094067 A094068 A094069 * A094071 A094072 A094073

Keyword

nonn

Author

N. J. A. Sloane, May 01 2004

Extensions

More terms from Ralf Stephan, Oct 14 2004

Status

approved