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A095844 Numerator of the integral of the n-th power of the Cantor function. 5
1, 1, 3, 1, 33, 5, 75, 611, 97653, 83057, 22018179, 9625216, 20894487717, 93120706729, 411117020063871, 297434062421057, 6650181371241300777, 6082551300359191981, 2198073713661546055399083 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

E. A. Gorin and B. N. Kukushkin, Integrals related to the Cantor function, St. Petersburg Math. J., 15, 449-468, 2004.

LINKS

Table of n, a(n) for n=0..18.

Eric Weisstein's World of Mathematics, Cantor Function

FORMULA

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

EXAMPLE

1, 1/2, 3/10, 1/5, 33/230, 5/46, 75/874, 611/8740, 97653/1673710, ...

MAPLE

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

MATHEMATICA

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-Fran├žois Alcover, Oct 23 2012, after Emeric Deutsch *)

CROSSREFS

Cf. A095845.

Sequence in context: A016481 A303818 A047815 * A113110 A317363 A190964

Adjacent sequences:  A095841 A095842 A095843 * A095845 A095846 A095847

KEYWORD

nonn,frac

AUTHOR

Eric W. Weisstein, Jun 08 2004

STATUS

approved

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Last modified June 17 06:06 EDT 2019. Contains 324183 sequences. (Running on oeis4.)