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A051711
a(0) = 1; for n > 0, a(n) = n!*4^n/2.
4
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
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.
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
KEYWORD
nonn,easy,nice,frac
EXTENSIONS
More terms from James A. Sellers, Dec 07 1999
Edited by Michael Somos, Aug 21 2002
STATUS
approved