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A091748 Generalized Bell numbers B_{6,2}. 3
1, 43, 5083, 1160113, 432168721, 238012552651, 181520958432283, 182989529196234433, 235492729726705299073, 376560458072018837889931, 732162019709408940671604091, 1700645336651586566571229542193 (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..12.

FORMULA

a(n)=sum(A091746(n, k), k=2..2*n)= sum((1/k!)*product(fallfac(k+4*(j-1), 2), j=1..n), k=2..infinity)/exp(1), n>=1. From eq.(9) of the Blasiak et al. reference with r=6, s=2. fallfac(n, m) := A008279(n, m) (falling factorials triangle). a(0) := 1 may be added.

MATHEMATICA

a[n_] := Sum[Product[FactorialPower[k+4*(j-1), 2], {j, 1, n}]/k!, {k, 2, Infinity}]/E; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 12}] (* Jean-Fran├žois Alcover, Sep 01 2016 *)

CROSSREFS

Cf. A072019 ( B_{5, 2}).

Sequence in context: A060485 A081795 A108837 * A208625 A147522 A183489

Adjacent sequences:  A091745 A091746 A091747 * A091749 A091750 A091751

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Feb 27 2004

STATUS

approved

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Last modified October 18 15:41 EDT 2021. Contains 348068 sequences. (Running on oeis4.)