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Search: id:A051711
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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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+0
2
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| 1, 2, 16, 192, 3072, 61440, 1474560, 41287680, 1321205760, 47563407360, 1902536294400, 83711596953600, 4018156653772800, 208944145996185600, 11700872175786393600, 702052330547183616000, 44931349155019751424000
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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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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.: (1-2x)/(1-4x). a(n)=4na(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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s=2; lst={1, s}; Do[s+=n*s+s; AppendTo[lst, s], {n, 6, 5!, 4}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 08 2008]
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PROGRAM
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(PARI) a(n)=if(n<1, !n, 4^n/2*n!)
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CROSSREFS
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Cf. A001662.
Sequence in context: A123898 A118644 A006335 this_sequence A012683 A012677 A158212
Adjacent sequences: A051708 A051709 A051710 this_sequence 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 (njas(AT)research.att.com).
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 07 1999
Edited by Michael Somos, Aug 21, 2002
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