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A103816
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Numerator of Sum_{k=1..n} (-1)^(k+1)/k!.
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3
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0, 1, 1, 2, 5, 19, 91, 177, 3641, 28673, 28319, 2523223, 27526069, 109339663, 4239014627, 59043418019, 26718637649, 14052333488521, 238063061452591, 158218865944829, 7358312808534631, 124213980448686521
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Numerator of (n!-A000166(n))/n!.
Numerator of 1 - A053557/A053556.
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LINKS
| Eric Weisstein's World of Mathematics, Continued Fraction Constant [From Eric W. Weisstein (eric(AT)weisstein.com), Oct 03 2008]
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FORMULA
| The Aitken delta-squared process leaves the sequence S(n)=Sum_{k=1..n} (-1)^(k+1)/k! essentially unchanged : S(n+3)=(S(n)*S(n+2)-(S(n+1))^2)/(S(n)+S(n+2)-2*S(n+1))
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MATHEMATICA
| Table[ Numerator[ Sum[ -(-1)^k/k!, {k, n}]], {n, 0, 22}] (* Robert G. Wilson v *)
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CROSSREFS
| Cf. A053556 (denominators).
Sequence in context: A205804 A052324 A020115 * A052169 A020019 A020109
Adjacent sequences: A103813 A103814 A103815 * A103817 A103818 A103819
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KEYWORD
| nonn,frac,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Apr 02 2005
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Oct 13 2005
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