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A091757 Generalized Bell numbers B_{8,2}. 2
1, 73, 15945, 6993073, 5124715761, 5641397595321, 8700819552421753, 17898786381229403105, 47345052327747786859873, 156535091017683923932912041, 632460052562874236182866885161 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

LINKS

Table of n, a(n) for n=1..11.

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.

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A176987 A174747 A210382 * A070531 A274591 A232293

Adjacent sequences:  A091754 A091755 A091756 * A091758 A091759 A091760

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Feb 27 2004

STATUS

approved

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Last modified October 26 02:14 EDT 2021. Contains 348256 sequences. (Running on oeis4.)