A287937 - OEIS

%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