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%I #12 Jun 26 2022 10:53:46
%S 1,4,20,119,819,6397,55919,541144,5746596,66475311,832418065,
%T 11222752125,162133146877,2499401777680,40960858008040,
%U 711240364356155,13045720176453587,252079975222183461,5118581045978055067,108972887981432267708,2427417968714846394712,56467770394205361146187
%N E.g.f.: exp(exp(x)-1)/(1-x)^3.
%C Sequence appears in the problem of normal ordering of functions of boson operators.
%H Harvey P. Dale, <a href="/A101055/b101055.txt">Table of n, a(n) for n = 0..447</a>
%H <a href="/index/La#Laguerre">Index entries for sequences related to Laguerre polynomials</a>
%F a(n) = ((-1)^n*n!/e)*Sum_{k>=0} L(n,-n-3,k)/k!, where L is a generalized Laguerre polynomial.
%F a(n) = (1/2)*Sum_{k=0..n} binomial(n,k)*(k + 2)!*Bell(n-k), where Bell() = A000110. - _Ilya Gutkovskiy_, May 24 2018
%F a(n) ~ exp(exp(1)-1) * n^2 * n! / 2. - _Vaclav Kotesovec_, Jun 26 2022
%t With[{nn=30},CoefficientList[Series[Exp[Exp[x]-1]/(1-x)^3,{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Aug 11 2021 *)
%Y Cf. A000110, A101053, A101054.
%K nonn
%O 0,2
%A _Karol A. Penson_, Nov 29 2004
%E Terms after a(15) from _Ilya Gutkovskiy_, May 24 2018
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