|
| |
|
|
A120268
|
|
Numerator of Sum[1/(2k-1)^2,{k,1,n}].
|
|
18
| |
|
|
1, 10, 259, 12916, 117469, 14312974, 2430898831, 487983368, 141433003757, 51174593563322, 51270597630767, 27164483940418988, 3400039831130408821, 30634921277843705014, 25789165074168004597399
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| a((p-1)/2) is divisible by prime p>3.
Denominators are A128492.
The limit of the rationals r(n):=Sum[1/(2k-1)^2,{k,1,n}] for n->infinity is (Pi^2)/8 = (1-1/2^2)*Zeta(2) which is approximately 1.233700550.
|
|
|
LINKS
| W. Lang, Rationals and limit.
|
|
|
FORMULA
| a(n) = numerator[Sum[1/(2k-1)^2,{k,1,n}]].
a(n) = Denominator of (Pi^2)/2 - Zeta[2,(2n-1)/2] [From Artur Jasinski (grafix(AT)csl.pl), Mar 03 2010]
|
|
|
MATHEMATICA
| Numerator[Table[Sum[1/(2k-1)^2, {k, 1, n}], {n, 1, 25}]]
|
|
|
CROSSREFS
| Cf. A025550, A007406.
Sequence in context: A100743 A126468 A024293 * A001824 A024294 A183406
Adjacent sequences: A120265 A120266 A120267 * A120269 A120270 A120271
|
|
|
KEYWORD
| frac,nonn
|
|
|
AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 01 2006
|
| |
|
|
