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A051711
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a(0) = 1; for n > 0, a(n) = n!*4^n/2.
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4
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1, 2, 16, 192, 3072, 61440, 1474560, 41287680, 1321205760, 47563407360, 1902536294400, 83711596953600, 4018156653772800, 208944145996185600, 11700872175786393600, 702052330547183616000, 44931349155019751424000
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OFFSET
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0,2
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COMMENTS
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For n <= 16, denominators in expansion of W(exp(x)) about x=1, where W is the Lambert function.
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LINKS
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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
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FORMULA
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E.g.f.: (1-2*x)/(1-4*x).
a(n) = 4*n * a(n-1), n > 0.
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EXAMPLE
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W(exp(x)) = 1 + (x-1)/2 + (x-1)^2/16 - (x-1)^3/192 - ... .
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MATHEMATICA
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Join[{1}, Table[(n! 4^n)/2, {n, 20}]] (* Harvey P. Dale, Oct 05 2012 *)
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PROG
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(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
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CROSSREFS
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Cf. A001662.
Sequence in context: A006335 A273591 A292347 * A274448 A209586 A334237
Adjacent sequences: A051708 A051709 A051710 * A051712 A051713 A051714
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KEYWORD
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nonn,easy,nice,frac
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from James A. Sellers, Dec 07 1999
Edited by Michael Somos, Aug 21 2002
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STATUS
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approved
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