A123525 Arises in the normal ordering of functions of a*(a+)*a, where a and a+ are the boson annihilation and creation operators, respectively.

2, 14, 102, 836, 7730, 79962, 916454, 11533832, 158149026, 2346622310, 37458934502, 640013453004, 11652216012242, 225169809833906, 4602407562991590, 99194703240441872

Offset: 1

Author

Karol A. Penson, Oct 02 2006

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..440

Crossrefs

Cf.: A002720, A052852, A123510, A123511, A123512, A123526, A123527.

Programs

Mathematica

Rest[With[{nmax = 50}, CoefficientList[Series[(1/(1 - x)^2)*Exp[x/(1 - x)]*LaguerreL[1, 1/(x - 1)]*x, {x, 0, nmax}], x]*Range[0, nmax]!]] (* G. C. Greubel, Oct 14 2017 *)

Formula

E.g.f.: (1/(1-x)^2)*exp(x/(1-x))*LaguerreL(1,1/(x-1))*x.

From Vaclav Kotesovec, Nov 13 2017: (Start)

Recurrence: (n-2)*(n-1)*a(n) = 2*(n-2)*n^2*a(n-1) - (n-1)^3*n*a(n-2).

a(n) ~ exp(2*sqrt(n) - n - 1/2) * n^(n + 5/4) / sqrt(2) * (1 + 31/(48*sqrt(n))).

(End)