This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A095845 #36 Feb 16 2025 08:32:53
%S A095845 1,2,10,5,230,46,874,8740,1673710,1673710,513828970,256914485,
%T A095845 631290272542,3156451362710,15513958447719650,12411166758175720,
%U A095845 305013731457236950790,305013731457236950790,119935974414957427604889850,3156209853025195463286575
%N A095845 Denominator of the integral of the n-th power of the Cantor function.
%H A095845 Amiram Eldar, <a href="/A095845/b095845.txt">Table of n, a(n) for n = 0..117</a>
%H A095845 E. A. Gorin and B. N. Kukushkin, <a href="https://doi.org/10.1090/S1061-0022-04-00817-9">Integrals related to the Cantor function</a>, St. Petersburg Math. J., 15, 449-468, 2004.
%H A095845 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CantorFunction.html">Cantor Function</a>.
%F A095845 The integral, a rational number, is given by J(n) = 1/(n+1) - Sum_{k = 1..floor(n/2)} binomial(n,2*k)*(2^(2*k-1)-1)*bernoulli(2*k)/((3*2^(2*k-1)-1)*(n-2*k+1)). - _Emeric Deutsch_, Feb 22 2005
%F A095845 Note that the Cantor function C(x) satisfies C(x) = C(3*x)/2 for x in [0,1/3], 1/2 for x in [1/3,2/3] and (1+C(3*x-2))/2 for x in [2/3,1]. Integrating both sides yields J(n) = (1 + Sum_{k=0..n-1} binomial(n,k)*J(k))/(3*2^n - 2) with J(0) = 1, where J(n) := Integral_{x=0..1} (C(x))^n dx. - _Jianing Song_, Nov 19 2023
%e A095845 1, 1/2, 3/10, 1/5, 33/230, 5/46, 75/874, 611/8740, 97653/1673710, ...
%p A095845 seq(denom(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..17); # _Emeric Deutsch_, Feb 22 2005
%t A095845 a[n_] := Denominator[1/(n + 1) - Sum[(Binomial[n, 2*k]*Floor[2^(2*k - 1) - 1]*BernoulliB[2*k])/Floor[(3*2^(2*k - 1) - 1)*(-2*k + n + 1)], {k, 1, Floor[n/2]}]]; Table[a[n], {n, 0, 17}] (* _Jean-François Alcover_, Oct 23 2012, after _Emeric Deutsch_ *)
%t A095845 f[0] = 1; f[1] = 1/2; f[n_] := f[n] = (1/(3*2^n - 2))*(2 + Sum[Binomial[n, k]*f[k], {k, 1, n - 1}]); Denominator[Array[f, 20, 0]] (* _Amiram Eldar_, Jan 26 2024 *)
%Y A095845 Cf. A095844 (numerators).
%K A095845 nonn,frac
%O A095845 0,2
%A A095845 _Eric W. Weisstein_, Jun 08 2004