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A123511
Arises in the normal ordering of functions of a*(a+)*a, where a and a+ are the boson annihilation and creation operators, respectively.
6
1, 8, 70, 680, 7315, 86576, 1119468, 15710640, 237885285, 3865865080, 67113398066, 1239550196248, 24267176759735, 501941612835040, 10936819334789720, 250370971426742496, 6007479214999260873
OFFSET
0,2
LINKS
FORMULA
E.g.f.: (1/(1-x)^4)*exp(x/(1-x))*LaguerreL(3,-x/(1-x)).
From Vaclav Kotesovec, Nov 13 2017: (Start)
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)
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Karol A. Penson, Oct 02 2006
EXTENSIONS
a(0)=1 prepended by G. C. Greubel, Oct 31 2017
STATUS
approved