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

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice
• frac

Comments

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

Examples

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

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

Crossrefs

Cf. A001662.

Programs

Magma

[1] cat [2^(2*n-1)*Factorial(n): n in [1..30]]; // G. C. Greubel, Mar 06 2018

Mathematica

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

PARI

a(n)=if(n<1,!n,4^n/2*n!)

Formula

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

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

Extensions

More terms from James Sellers, Dec 07 1999

Edited by Michael Somos, Aug 21 2002