cp's OEIS Frontend

A288163 Integers related to the half moments of Rvachëv function.

%I A288163 #19 Apr 05 2018 13:38:58
%S A288163 1,1,5,84,4004,494760,150120600,107969547840,179605731622464,
%T A288163 678695382464158080,5745964983105758544000,
%U A288163 107798142804281290451059200,4441362930723337358985334172160,398854836980938754158182857661404160,77576833096847783279235708819073596288000
%N A288163 Integers related to the half moments of Rvachëv function.
%C A288163 These numbers determine the half moments 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.
%H A288163 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 A288163 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 A288163 a(n) = (n+1)!*Product_{k=1..n}(2^k-1)*d(n) where d(n) are the rationals defined by the recurrence d(0)=1; d(n)=Sum_{k=0..n-1}[binomial(n+1,k)d(k)]/((n+1)*(2^n-1)) (cf. A288161).
%t A288163 d[0] = 1;
%t A288163 d[n_] := d[n] =
%t A288163   Sum[Binomial[n + 1, k] d[k], {k, 0, n - 1}]/((n + 1)*(2^n - 1));
%t A288163 a[n_] := (n + 1)! Product[(2^k - 1), {k, 1, n}] d[n];
%t A288163 Table[a[n], {n, 0, 14}]
%Y A288163 Cf. A287936, A287937, A287938, A288161.
%K A288163 nonn
%O A288163 0,3
%A A288163 _Juan Arias-de-Reyna_, Jun 06 2017