A091757 Generalized Bell numbers B_{8,2}.

1, 73, 15945, 6993073, 5124715761, 5641397595321, 8700819552421753, 17898786381229403105, 47345052327747786859873, 156535091017683923932912041, 632460052562874236182866885161

Offset: 1

Author

Wolfdieter Lang, Feb 27 2004

Keywords

• nonn
• easy

References

• P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem, Phys. Lett. A 309 (2003) 198-205.
• M. Schork, On the combinatorics of normal ordering bosonic operators and deforming it, J. Phys. A 36 (2003) 4651-4665.

Crossrefs

Cf. A091749 (B_{7, 2}).

Programs

Mathematica

a[n_] := Sum[Product[FactorialPower[k+6*(j-1), 2], {j, 1, n}]/k!, {k, 2, Infinity}]/E; Array[a, 11] (* Jean-François Alcover, Sep 01 2016 *)

Formula

a(n)=sum(A092077(n, k), k=2..2*n)= sum((1/k!)*product(fallfac(k+6*(j-1), 2), j=1..n), k=2..infinity)/exp(1), n>=1. From eq.(9) of the Blasiak et al. reference with r=8, s=2. fallfac(n, m) := A008279(n, m) (falling factorials triangle). a(0) := 1 may be added.