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%I #11 Jun 24 2016 07:59:25
%S 1,2,16,192,3072,61440,1474560,41287680,1321205760,47563407360,
%T 1902536294400,83711596953600,4018156653772800,208944145996185600,
%U 11700872175786393600,702052330547183616000,44931349155019751424000,235025518657026392064000,219983885462976702971904000,16718775295186229425864704000,1337502023614898354069176320000
%N Denominators in expansion of W(exp(x)) about x=1, where W is the Lambert function.
%C a(17) is the first term that differs from A051711.
%H R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, <a href="http://www.apmaths.uwo.ca/~rcorless/frames/PAPERS/LambertW/LambertW.ps">On the Lambert W Function</a>, Advances in Computational Mathematics, (5), 1996, pp. 329-359.
%H R. M. Corless, D. J. Jeffrey and D. E. Knuth, <a href="http://www.apmaths.uwo.ca/~rcorless/frames/PAPERS/LambertW/CorlessJeffreyKnuth.ps">A sequence of series for the Lambert W Function</a> (section 2.2).
%F a(n) = A051711(n)/gcd(A001662(n),A051711(n))
%e W(exp(x)) = 1 +(x-1)/2+(x-1)^2/16-(x-1)^3/192-...
%p a:= n-> denom(coeftayl(LambertW(exp(x)), x=1, n)):
%p seq(a(n), n=0..30); # _Alois P. Heinz_, Nov 08 2012
%t CoefficientList[ Series[ ProductLog[ Exp[1+x] ], {x, 0, 22}], x] // Denominator (* _Jean-François Alcover_, Oct 15 2012 *)
%Y Cf. A274447.
%K nonn,easy,frac
%O 0,2
%A _Paolo Bonzini_, Jun 23 2016
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