A051711 a(0) = 1; for n > 0, a(n) = n!*4^n/2.

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

Offset

0,2

Comments

For n <= 16, denominators in expansion of W(exp(x)) about x=1, where W is the Lambert function.

Links

G. C. Greubel, Table of n, a(n) for n = 0..365

J. M. Borwein and R. M. Corless, Emerging tools for experimental mathematics.

J. M. Borwein and R. M. Corless, Emerging tools for experimental mathematics, Amer. Math. Monthly, 106 (No. 10, 1999), 889-909.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 647

Formula

E.g.f.: (1-2*x)/(1-4*x).

a(n) = 4*n * a(n-1), n > 0.

Example

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

Mathematica

Join[{1}, Table[(n! 4^n)/2, {n, 20}]] (* Harvey P. Dale, Oct 05 2012 *)

Prog

(PARI) a(n)=if(n<1, !n, 4^n/2*n!)
(Magma) [1] cat [2^(2*n-1)*Factorial(n): n in [1..30]]; // G. C. Greubel, Mar 06 2018

Crossrefs

Cf. A001662.

Sequence in context: A006335 A273591 A292347 * A274448 A209586 A334237

Adjacent sequences: A051708 A051709 A051710 * A051712 A051713 A051714

Keyword

nonn,easy,nice,frac

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, Dec 07 1999

Edited by Michael Somos, Aug 21 2002

Status

approved