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Search: id:A005429
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| A005429 |
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Ap\*'ery numbers: n^3*C(2n,n).
(Formerly M2169)
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+0
7
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| 0, 2, 48, 540, 4480, 31500, 199584, 1177176, 6589440, 35443980, 184756000, 938929992, 4672781568, 22850118200, 110079950400, 523521630000, 2462025277440, 11465007358860, 52926189069600, 242433164404200, 1102772230560000, 4984806175188840, 22404445765690560
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.6.3.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A. J. van der Poorten, A proof that Euler missed...Apery's proof of the irrationality of zeta(3), Math. Intelligencer 1 (1978/1979), 195-203.
I. J. Zucker, On the series $ Sum\sp \infty\sb {k=1}(\sp{2k}\sb {\; k})\sp {-1}k\sp{-n}$ and related sums, J. Number Theory 20 (1985), no. 1, 92-102.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..200
M. Kondratiewa and S. Sadov, Markov's transformation of series and the WZ method
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FORMULA
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Sum_{ n >= 1} (-1)^(n+1) / a(n) = 2 zeta(3) / 5.
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MAPLE
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with(combinat):for n from 0 to 22 do printf(`%d, `, n^2*sum(binomial(2*n, n), k=1..n)) od: - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 13 2007
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CROSSREFS
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Cf. A002736, A005258, A005259, A005429, A005430.
Adjacent sequences: A005426 A005427 A005428 this_sequence A005430 A005431 A005432
Sequence in context: A101362 A058090 A051252 this_sequence A035606 A157057 A009670
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KEYWORD
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nonn,nice,easy
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AUTHOR
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Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
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Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Apr 06 2004
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