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A091749
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Generalized Bell numbers B_{7,2}.
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3
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1, 57, 9367, 3039037, 1631142633, 1306299636853, 1458563053824871, 2164056543968020185, 4116264432907357578961, 9762542731516508922640177, 28237035023990471230544779095, 97815632146487780258222172635029
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OFFSET
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1,2
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REFERENCES
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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.
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LINKS
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Table of n, a(n) for n=1..12.
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FORMULA
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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.
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MATHEMATICA
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a[n_] := Sum[Product[FactorialPower[k+5*(j-1), 2], {j, 1, n}]/k!, {k, 2, Infinity}]/E; Array[a, 12] (* Jean-François Alcover, Sep 01 2016 *)
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CROSSREFS
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Cf. A091748 (B_{6, 2}).
Sequence in context: A263669 A286442 A219077 * A218425 A094777 A218662
Adjacent sequences: A091746 A091747 A091748 * A091750 A091751 A091752
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang, Feb 27 2004
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STATUS
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approved
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