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A123511
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Arises in the normal ordering of functions of a*(a+)*a, where a and a+ are the boson annihilation and creation operators, respectively.
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6
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1, 8, 70, 680, 7315, 86576, 1119468, 15710640, 237885285, 3865865080, 67113398066, 1239550196248, 24267176759735, 501941612835040, 10936819334789720, 250370971426742496, 6007479214999260873
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OFFSET
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0,2
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LINKS
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FORMULA
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E.g.f.: (1/(1-x)^4)*exp(x/(1-x))*LaguerreL(3,-x/(1-x)).
Recurrence: n*a(n) = 2*n*(n+3)*a(n-1) - (n-1)*(n+2)*(n+3)*a(n-2).
a(n) ~ exp(2*sqrt(n)-n-1/2) * n^(n + 13/4) / (3*2^(3/2)) * (1 + 31/(48*sqrt(n))).
(End)
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MATHEMATICA
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max = 16; s = (1/(1 - x)^4)*Exp[x/(1 - x)]*LaguerreL[3, -x/(1 - x)] + O[x]^(max + 1); CoefficientList[s, x]*Range[0, max]! (* Jean-François Alcover, May 23 2016 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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