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A123525 Arises in the normal ordering of functions of a*(a+)*a, where a and a+ are the boson annihilation and creation operators, respectively. 3
2, 14, 102, 836, 7730, 79962, 916454, 11533832, 158149026, 2346622310, 37458934502, 640013453004, 11652216012242, 225169809833906, 4602407562991590, 99194703240441872 (list; graph; refs; listen; history; text; internal format)
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 A293044

Adjacent sequences:  A123522 A123523 A123524 * A123526 A123527 A123528

KEYWORD

nonn

AUTHOR

Karol A. Penson, Oct 02 2006

STATUS

approved

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Last modified June 25 12:55 EDT 2019. Contains 324352 sequences. (Running on oeis4.)