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

1,1

Links

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

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)

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 *)

Crossrefs

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

Sequence in context: A037726 A037621 A085372 * A286310 A295865 A355069

Adjacent sequences: A123522 A123523 A123524 * A123526 A123527 A123528

Keyword

nonn

Author

Karol A. Penson, Oct 02 2006

Status

approved