|
Search: id:A130416
|
|
|
| A130416 |
|
Numerator of partial sums for a series of (17/18)*Zeta(4)= (17/1680)*Pi^4. |
|
+0
2
|
|
| 1, 49, 6623, 741857, 13247611, 3060203141, 13645449045719, 218327192834879, 100212182125865461, 1904031462407822767, 2534265876944902342877, 58288115171766608401171, 128058989033214718801833487
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Denominators are given by A130417.
The rationals r(n):=2*sum(1/((k^4)*binomial(2*k,k)),k=1..n) tend, in the limit n->infinity, to (18/17)*Zeta(4) = (17/1680)*Pi^4, approximately 1.022194166.
|
|
REFERENCES
|
L. Berggren, T. Borwein and P. Borwein, Pi: A Source Book, Springer, New York, 1997, p. 687.
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 89, Exercise.
A. van der Poorten, A proof that Euler missed..., Math. Intell. 1(1979)195-203; reprinted in Pi: A Source Book, pp. 439-447, footnote 10, p. 446 (conjecture).
|
|
LINKS
|
W. Lang, Rationals and limit.
|
|
FORMULA
|
a(n)=numerator(r(n)), n>=1, with the rationals defined above.
|
|
EXAMPLE
|
Rationals [1, 49/48, 6623/6480, 741857/725760, 13247611/12960000,...].
|
|
CROSSREFS
|
Partial sums for Zeta(4): A007410/A007480.
Sequence in context: A053772 A075416 A127861 this_sequence A006692 A014801 A094199
Adjacent sequences: A130413 A130414 A130415 this_sequence A130417 A130418 A130419
|
|
KEYWORD
|
nonn,frac,easy
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jul 13 2007
|
|
|
Search completed in 0.002 seconds
|
