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A095844
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Numerator of the integral of the n-th power of the Cantor function.
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5
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1, 1, 3, 1, 33, 5, 75, 611, 97653, 83057, 22018179, 9625216, 20894487717, 93120706729, 411117020063871, 297434062421057, 6650181371241300777, 6082551300359191981, 2198073713661546055399083
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OFFSET
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0,3
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REFERENCES
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E. A. Gorin and B. N. Kukushkin, Integrals related to the Cantor function, St. Petersburg Math. J., 15, 449-468, 2004.
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LINKS
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Table of n, a(n) for n=0..18.
Eric Weisstein's World of Mathematics, Cantor Function
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FORMULA
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The integral, a rational number, is given by J(n)=1/(n+1)-sum(binomial(n, 2k)[2^(2k-1)-1]bernoulli(2k)/[(3*2^(2k-1)-1)(n-2k+1)], k = 1 .. floor(n/2)). - Emeric Deutsch, Feb 22 2005
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EXAMPLE
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1, 1/2, 3/10, 1/5, 33/230, 5/46, 75/874, 611/8740, 97653/1673710, ...
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MAPLE
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seq(numer(1/(n+1)-sum(binomial(n, 2*k)*(2^(2*k-1)-1)*bernoulli(2*k)/(3*2^(2*k-1)-1)/(n-2*k+1), k = 1 .. floor(1/2*n))), n=1..18); # Emeric Deutsch
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MATHEMATICA
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a[n_] := Numerator[ 1/(n+1) - Sum[Binomial[n, 2 k]*Floor[2^(2k - 1) - 1]*BernoulliB[2k]/Floor[(3*2^(2k - 1) - 1)*(n - 2k + 1)], {k, 1, Floor[n/2]}]]; Table[a[n], {n, 0, 18}] (* Jean-François Alcover, Oct 23 2012, after Emeric Deutsch *)
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CROSSREFS
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Cf. A095845.
Sequence in context: A016481 A303818 A047815 * A113110 A317363 A190964
Adjacent sequences: A095841 A095842 A095843 * A095845 A095846 A095847
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KEYWORD
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nonn,frac
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AUTHOR
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Eric W. Weisstein, Jun 08 2004
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STATUS
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approved
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