|
%I #19 Nov 13 2017 09:05:52
%S 1,8,70,680,7315,86576,1119468,15710640,237885285,3865865080,
%T 67113398066,1239550196248,24267176759735,501941612835040,
%U 10936819334789720,250370971426742496,6007479214999260873
%N Arises in the normal ordering of functions of a*(a+)*a, where a and a+ are the boson annihilation and creation operators, respectively.
%H G. C. Greubel, <a href="/A123511/b123511.txt">Table of n, a(n) for n = 0..440</a>
%F E.g.f.: (1/(1-x)^4)*exp(x/(1-x))*LaguerreL(3,-x/(1-x)).
%F From _Vaclav Kotesovec_, Nov 13 2017: (Start)
%F Recurrence: n*a(n) = 2*n*(n+3)*a(n-1) - (n-1)*(n+2)*(n+3)*a(n-2).
%F a(n) ~ exp(2*sqrt(n)-n-1/2) * n^(n + 13/4) / (3*2^(3/2)) * (1 + 31/(48*sqrt(n))).
%F (End)
%t 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 *)
%Y Cf. A002720, A052852, A123510, A123512.
%K nonn
%O 0,2
%A _Karol A. Penson_, Oct 02 2006
%E a(0)=1 prepended by _G. C. Greubel_, Oct 31 2017
| 