OFFSET
0,3
COMMENTS
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.
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));
a[n_] := a[n] = c[n] (2 n + 1)!! Product[(2^(2 k) - 1), {k, 1, n}];
Table[a[n], {n, 0, 30}]
Table[(-1)^n 4^(-n) (2 n)! (2 n + 1)!! Sum[QBinomial[n, k, 1/4] 2^(-k (3 k + 1)/2)/(2 n + k + 1)! Sum[(-1)^ThueMorse[m] (2 m + 1)^(2 n + k + 1), {m, 0, 2^k - 1}], {k, 0, n}], {n, 0, 12}] (* Vladimir Reshetnikov, Jul 08 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Juan Arias-de-Reyna, Jun 03 2017
STATUS
approved