A123511 Arises in the normal ordering of functions of a*(a+)*a, where a and a+ are the boson annihilation and creation operators, respectively.

1, 8, 70, 680, 7315, 86576, 1119468, 15710640, 237885285, 3865865080, 67113398066, 1239550196248, 24267176759735, 501941612835040, 10936819334789720, 250370971426742496, 6007479214999260873

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..440

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

Cf. A002720, A052852, A123510, A123512.

Sequence in context: A299938 A152263 A142986 * A322416 A287482 A053729

Adjacent sequences: A123508 A123509 A123510 * A123512 A123513 A123514

Keyword

nonn

Author

Karol A. Penson, Oct 02 2006

Extensions

a(0)=1 prepended by G. C. Greubel, Oct 31 2017

Status

approved