|
|
A288163
|
|
Integers related to the half moments of Rvachëv function.
|
|
0
|
|
|
1, 1, 5, 84, 4004, 494760, 150120600, 107969547840, 179605731622464, 678695382464158080, 5745964983105758544000, 107798142804281290451059200, 4441362930723337358985334172160, 398854836980938754158182857661404160, 77576833096847783279235708819073596288000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
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.
|
|
LINKS
|
|
|
FORMULA
|
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).
|
|
MATHEMATICA
|
d[0] = 1;
d[n_] := d[n] =
Sum[Binomial[n + 1, k] d[k], {k, 0, n - 1}]/((n + 1)*(2^n - 1));
a[n_] := (n + 1)! Product[(2^k - 1), {k, 1, n}] d[n];
Table[a[n], {n, 0, 14}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|