login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Denominator of moments of Rvachëv function up(x).
4

%I #18 Jun 21 2017 04:35:40

%S 1,9,675,59535,32531625,24405225075,4133856862760625,

%T 2232691548877164375,13301767332333178846875,

%U 100028040755473167511640090625,182171989134769427819794434994453125,12012265189685856975048179723754213046875,75749878923357625026812035792140968086378130859375

%N Denominator of moments of Rvachëv function up(x).

%H J. Arias de Reyna, <a href="https://arxiv.org/abs/1702.05442">An infinitely differentiable function with compact support:Definition and properties</a>, arXiv:1702.05442 [math.CA], 2017.

%H J. Arias de Reyna, <a href="https://arxiv.org/abs/1702.06487">Arithmetic of the Fabius function</a>, arXiv:1702.06487 [math.NT], 2017.

%F Recurrence c(0)=1, c(n)=Sum_{k=0..n-1}(binomial(2n+1,2k) c_k)/((2n+1)*(2^(2n)-1)), where c(n)=A287936(n)/a(n).

%e A287936(n)/a(n) = 1/1, 1/9, 19/675, 583/59535, ...

%t c[0] = 1;

%t c[n_] := c[n] =

%t Sum[Binomial[2 n + 1, 2 k] c[k], {k, 0, n - 1}]/((2 n + 1) (2^(2 n) - 1));

%t Table[Denominator[c[n]], {n, 0, 30}]

%Y Cf. A287936, A287938.

%K nonn,frac

%O 0,2

%A _Juan Arias-de-Reyna_, Jun 03 2017