cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A123525 #7 Nov 13 2017 09:20:45
%S A123525 2,14,102,836,7730,79962,916454,11533832,158149026,2346622310,
%T A123525 37458934502,640013453004,11652216012242,225169809833906,
%U A123525 4602407562991590,99194703240441872
%N A123525 Arises in the normal ordering of functions of a*(a+)*a, where a and a+ are the boson annihilation and creation operators, respectively.
%H A123525 G. C. Greubel, <a href="/A123525/b123525.txt">Table of n, a(n) for n = 1..440</a>
%F A123525 E.g.f.: (1/(1-x)^2)*exp(x/(1-x))*LaguerreL(1,1/(x-1))*x.
%F A123525 From _Vaclav Kotesovec_, Nov 13 2017: (Start)
%F A123525 Recurrence: (n-2)*(n-1)*a(n) = 2*(n-2)*n^2*a(n-1) - (n-1)^3*n*a(n-2).
%F A123525 a(n) ~ exp(2*sqrt(n) - n - 1/2) * n^(n + 5/4) / sqrt(2) * (1 + 31/(48*sqrt(n))).
%F A123525 (End)
%t A123525 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 *)
%Y A123525 Cf.: A002720, A052852, A123510, A123511, A123512, A123526, A123527.
%K A123525 nonn
%O A123525 1,1
%A A123525 _Karol A. Penson_, Oct 02 2006