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

Author

Paolo Bonzini, Jun 23 2016

Keywords

• nonn
• easy
• frac

Comments

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

Examples

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

Links

• 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).

Crossrefs

Cf. A274447.

Programs

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 *)

Formula

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