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A091749 Generalized Bell numbers B_{7,2}. 3
1, 57, 9367, 3039037, 1631142633, 1306299636853, 1458563053824871, 2164056543968020185, 4116264432907357578961, 9762542731516508922640177, 28237035023990471230544779095, 97815632146487780258222172635029 (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(A091747(n, k), k=2..2*n)= sum((1/k!)*product(fallfac(k+5*(j-1), 2), j=1..n), k=2..infinity)/exp(1), n>=1. From eq.(9) of the Blasiak et al. reference with r=7, s=2. fallfac(n, m) := A008279(n, m) (falling factorials triangle). a(0) := 1 may be added.

MATHEMATICA

a[n_] := Sum[Product[FactorialPower[k+5*(j-1), 2], {j, 1, n}]/k!, {k, 2, Infinity}]/E; Array[a, 12] (* Jean-Fran├žois Alcover, Sep 01 2016 *)

CROSSREFS

Cf. A091748 (B_{6, 2}).

Sequence in context: A263669 A286442 A219077 * A218425 A094777 A218662

Adjacent sequences:  A091746 A091747 A091748 * A091750 A091751 A091752

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Feb 27 2004

STATUS

approved

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Last modified November 26 21:07 EST 2021. Contains 349344 sequences. (Running on oeis4.)