|
|
A103347
|
|
Numerators of Sum_{k=1..n} 1/k^7 = Zeta(7,n).
|
|
6
|
|
|
1, 129, 282251, 36130315, 2822716691183, 940908897061, 774879868932307123, 99184670126682733619, 650750755630450535274259, 650750820166709327386387, 12681293156341501091194786541177, 12681293507322704937269896541177
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
a(n) gives the partial sums, Zeta(7,n), of Euler's Zeta(7). Zeta(k,n) is also called H(k,n) because for k=1 these are the harmonic numbers H(n) A001008/A002805.
For the denominators see A103348 and for the rationals Zeta(7,n) see the W. Lang link under A103345.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = numerator(sum_{k=1..n} 1/k^7).
G.f. for rationals Zeta(7, n): polylogarithm(7, x)/(1-x).
|
|
MAPLE
|
f:= n -> numer(Psi(6, n+1)/720 + Zeta(7)):
|
|
MATHEMATICA
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,frac,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|