cp's OEIS Frontend

A287936 Numerator of moments of Rvachëv function up(x).

%I A287936 #19 Jun 21 2017 04:23:28
%S A287936 1,1,19,583,132809,46840699,4068990560161,1204567303451311,
%T A287936 4146897304424408411,18814360006695807527868793,
%U A287936 21431473463327429953796293981397,911368783375270623395381542054690099,3805483535214088799368825731508632105336401423
%N A287936 Numerator of moments of Rvachëv function up(x).
%C A287936 a(n)/A287937(n) is equal to the integral of t^(2n) * up(t), the moment of the Rvachëv function. The Rvachëv function is related to the Fabius function; up(x)=F(x+1) for |x|<1 and up(x)=0 for |x|>=1, where F is the Fabius function.
%H A287936 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 A287936 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 A287936 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)=a(n)/A287937(n).
%t A287936 c[0] = 1;
%t A287936 c[n_] := c[n] =
%t A287936    Sum[Binomial[2 n + 1, 2 k] c[k], {k, 0, n - 1}]/((2 n + 1) (2^(2 n) - 1));
%t A287936 Table[Numerator[c[n]], {n, 0, 30}]
%Y A287936 Cf. A287937, A287938.
%K A287936 nonn,frac
%O A287936 0,3
%A A287936 _Juan Arias-de-Reyna_, Jun 03 2017