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A087617
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Gabcke sequence: a(0)=1; (n+1) a(n+1) = Sum_{k=0..n} 2^(4k+1) |E(2k+2)| a(n-k), where |E(2k+2)| are Euler numbers (E(2k)=(-1)^k A000364(k)).
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0
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1, 2, 82, 10572, 2860662, 1330910844, 947622146676, 957663025230936, 1303349182536886566, 2298001401440208011756, 5095053865489946980238428, 13874003700656227505945514920, 45517269584820569745186971856060
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The recurrence does not imply that these numbers are integers. Gabcke conjectured that they are integers. This is proved in Arias de Reyna, 'Dynamical zeta functions and Kummer congruences'. They also appear as the coefficients of the asymptotic expansion Sum a(n) tau^(4n) n=0...infinity of the function Re log Gamma(1/4 +it/2) + Pi t/4 +(1/4)log(t/2) -log sqrt(2Pi), where tau=1/2sqrt(2t)
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REFERENCES
| W. Gabcke, Neue Herleitung und explizite Restabschaetzung der Riemann-Siegel-Formel. Dissertation, Univ. Goettingen (1979)
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LINKS
| J. Arias de Reyna, Dynamical zeta functions and Kummer congruences .
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MATHEMATICA
| lambda[0] = 1; lambda[n_] := lambda[n] = Sum[2^(4 k + 1) Abs[EulerE[2k + 2]]lambda[n - 1 - k], {k, 0, n - 1}]/n
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CROSSREFS
| Sequence in context: A197641 A093666 A063270 * A140157 A139867 A090434
Adjacent sequences: A087614 A087615 A087616 * A087618 A087619 A087620
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KEYWORD
| easy,nonn,nice
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AUTHOR
| Juan Arias de Reyna (arias(AT)us.es), Sep 12 2003
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