|
Search: id:A089638
|
|
|
| A089638 |
|
Numerator of (5/2)*Sum_{i=1..n} (-1)^(i-1)/(i^3*C(2*i,i)). |
|
+0
2
|
|
| 0, 5, 115, 1039, 58157, 1454021, 6854599, 30564710941, 244517610353, 37411196579209, 64619338818497, 86008340157931507, 8951094220597141, 334314418075511195849, 334314418069194908729, 48475590620225838341897, 707173321988579559023843
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Related to Apery's proof of the irrationality of zeta(3).
|
|
REFERENCES
|
C. Elsner, On recurrence formulae for sums involving binomial coefficients, Fib. Q., 43 (No. 1, 2005), 31-45.
|
|
FORMULA
|
(5/2)*Sum_{i=1..infinity} (-1)^(i-1)/(i^3*C(2*i, i)) = zeta(3).
|
|
EXAMPLE
|
0, 5/4, 115/96, 1039/864, 58157/48384, 1454021/1209600, 6854599/5702400, ... -> zeta(3).
|
|
PROGRAM
|
(PARI) a(n)=numerator(5/2*sum(k=1, n, (-1)^(k+1)/k^3/binomial(2*k, k)))
|
|
CROSSREFS
|
Cf. A002117, A089639.
Adjacent sequences: A089635 A089636 A089637 this_sequence A089639 A089640 A089641
Sequence in context: A009691 A053712 A091026 this_sequence A109057 A080988 A006221
|
|
KEYWORD
|
nonn,frac
|
|
AUTHOR
|
Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 01 2004
|
|
EXTENSIONS
|
Edited by njas, Aug 23 2008 at the suggestion of R. J. Mathar
|
|
|
Search completed in 0.002 seconds
|
