|
Search: id:A130551
|
|
|
| A130551 |
|
Numerators of partial sums for a series of (4/5)*Zeta(3). |
|
+0
4
|
|
| 1, 23, 1039, 58157, 1454021, 6854599, 30564710941, 244517610353, 37411196579209, 64619338818497, 86008340157931507, 8951094220597141, 334314418075511195849, 334314418069194908729, 48475590620225838341897
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
The rationals r(n):=2*sum(((-1)^(j-1))/((j^3)*binomial(2*j,j)),j=1..n), tend for n->infinity, to (4/5)*Zeta(3), which is approximately 0.9616455224. See the van der Poorten reference.
The denominators are given in A130552.
|
|
REFERENCES
|
A. van der Poorten, A proof that Euler missed..., Math. Intell. 1(1979)195-203; reprinted in Pi: A Source Book, pp. 439-447, eq. 2, with a proof in section 3 and further references in footnote 4.
L. Berggren, T. Borwein and P. Borwein, Pi: A Source Book, Springer, New York, 1997, p. 687.
|
|
LINKS
|
W. Lang, Rationals and limit.
|
|
FORMULA
|
a(n)=numerator(r(n)), n>=1, with the rationals r(n) defined above and taken in lowest terms.
|
|
EXAMPLE
|
Rationals r(n): [1, 23/24, 1039/1080, 58157/60480, 1454021/1512000,...].
|
|
CROSSREFS
|
Adjacent sequences: A130548 A130549 A130550 this_sequence A130552 A130553 A130554
Sequence in context: A008961 A139193 A077283 this_sequence A069479 A042015 A042012
|
|
KEYWORD
|
nonn,frac,easy
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jul 13 2007
|
|
|
Search completed in 0.002 seconds
|
