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

1, 1, 19, 583, 132809, 46840699, 4068990560161, 1204567303451311, 4146897304424408411, 18814360006695807527868793, 21431473463327429953796293981397, 911368783375270623395381542054690099, 3805483535214088799368825731508632105336401423

Offset: 0

Author

Juan Arias-de-Reyna, Jun 03 2017

Keywords

• nonn
• frac

Comments

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.

Links

• J. Arias de Reyna, An infinitely differentiable function with compact support:Definition and properties, arXiv:1702.05442 [math.CA], 2017.
• J. Arias de Reyna, Arithmetic of the Fabius function, arXiv:1702.06487 [math.NT], 2017.

Crossrefs

Cf. A287937, A287938.

Programs

Mathematica

c[0] = 1;
c[n_] := c[n] =
   Sum[Binomial[2 n + 1, 2 k] c[k], {k, 0, n - 1}]/((2 n + 1) (2^(2 n) - 1));
Table[Numerator[c[n]], {n, 0, 30}]

Formula

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).