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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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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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KEYWORD
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nonn,easy,nice,frac
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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