A274448 Denominators in expansion of W(exp(x)) about x=1, where W is the Lambert function.

1, 2, 16, 192, 3072, 61440, 1474560, 41287680, 1321205760, 47563407360, 1902536294400, 83711596953600, 4018156653772800, 208944145996185600, 11700872175786393600, 702052330547183616000, 44931349155019751424000, 235025518657026392064000, 219983885462976702971904000, 16718775295186229425864704000, 1337502023614898354069176320000

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 A334237 A356585

Adjacent sequences: A274445 A274446 A274447 * A274449 A274450 A274451

Keyword

nonn,easy,frac

Author

Paolo Bonzini, Jun 23 2016

Status

approved