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A274448 Denominators in expansion of W(exp(x)) about x=1, where W is the Lambert function. 2
1, 2, 16, 192, 3072, 61440, 1474560, 41287680, 1321205760, 47563407360, 1902536294400, 83711596953600, 4018156653772800, 208944145996185600, 11700872175786393600, 702052330547183616000, 44931349155019751424000, 235025518657026392064000, 219983885462976702971904000, 16718775295186229425864704000, 1337502023614898354069176320000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(17) is the first term that differs from A051711.

LINKS

Table of n, a(n) for n=0..20.

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, On the Lambert W Function, Advances in Computational Mathematics, (5), 1996, pp. 329-359.

R. M. Corless, D. J. Jeffrey and D. E. Knuth, A sequence of series for the Lambert W Function (section 2.2).

FORMULA

a(n) = A051711(n)/gcd(A001662(n),A051711(n))

EXAMPLE

W(exp(x)) = 1 +(x-1)/2+(x-1)^2/16-(x-1)^3/192-...

MAPLE

a:= n-> denom(coeftayl(LambertW(exp(x)), x=1, n)):

seq(a(n), n=0..30);  # Alois P. Heinz, Nov 08 2012

MATHEMATICA

CoefficientList[ Series[ ProductLog[ Exp[1+x] ], {x, 0, 22}], x] // Denominator (* Jean-François Alcover, Oct 15 2012 *)

CROSSREFS

Cf. A274447.

Sequence in context: A273591 A292347 A051711 * A209586 A012683 A012677

Adjacent sequences:  A274445 A274446 A274447 * A274449 A274450 A274451

KEYWORD

nonn,easy,frac

AUTHOR

Paolo Bonzini, Jun 23 2016

STATUS

approved

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Last modified November 14 15:15 EST 2019. Contains 329126 sequences. (Running on oeis4.)