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Search: id:A130549
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| A130549 |
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Numerators of partial sums for a series for 2*Zeta(2)/3 = (Pi^2)/9. |
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+0
4
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| 1, 13, 197, 1105, 9211, 130277, 82987349, 331950131, 16929464521, 29241805241, 3538258509761, 6259995854281, 1057939300471201, 1057939300716589, 51133732870640471, 372975463296151087, 107789908892879155343
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OFFSET
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1,2
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COMMENT
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Denominators are given in A130550.
The r(n):= 2*sum(1/(j^2*binomial(2*j,j)),j=1..n) tend, for n->infinity, to 2*Zeta(2)/3 = (Pi^2)/9, which is approximately 1.096622711.
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REFERENCES
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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 hint for the proof in footnote 4.
L. Berggren, T. Borwein and P. Borwein, Pi: A Source Book, Springer, New York, 1997, p. 687.
C. Elsner, On recurrence formulae for sums involving binomial coefficients, Fib. Q., 43 (No. 1, 2005), 31-45.
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LINKS
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W. Lang, Rationals and limit.
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FORMULA
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a(n)=numerator(r(n)), n>=1, with the rationals r(n) defined above.
Numerator of (2/3)* Sum_{i=1..n} 1/(i^2*C(2*i,i)). - Wolfdieter Lang, Oct 07 2008
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EXAMPLE
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Rationals r(n): [1, 13/12, 197/180, 1105/1008, 9211/8400, 130277/118800,...].
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CROSSREFS
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Cf. A112099, A112100, A112102, A112103, A130550.
Sequence in context: A099271 A081796 A140536 this_sequence A055478 A121503 A014404
Adjacent sequences: A130546 A130547 A130548 this_sequence A130550 A130551 A130552
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KEYWORD
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nonn,frac,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jul 13 2007
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