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Search: id:A059416
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| A059416 |
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Denominators of sequence arising from Apery's proof that zeta(3) is irrational. |
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4
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| 1, 1, 4, 36, 288, 36000, 800, 1372000, 2195200, 2667168000, 2667168000, 28400004864, 3550000608000, 311974053431040, 7799351335776000, 7799351335776000, 1134451103385600, 306545704901339904000, 6812126775585331200, 233621887768698933504000
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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M. Kontsevich and D. Zagier, Periods, pp. 771-808 of B. Engquist and W. Schmid, editors, Mathematics Unlimited - 2001 and Beyond, 2 vols., Springer-Verlag, 2001.
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LINKS
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V. Strehl, Recurrences and Legendre transform
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FORMULA
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(n+1)^3*a(n+1) = (34*n^3 + 51*n^2 + 27*n +5)*a(n) - n^3*a(n-1), n >= 1.
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EXAMPLE
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0, 6, 351/4, 62531/36, ...
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MAPLE
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a := proc(n) option remember; if n=0 then 0 elif n=1 then 6 else (n^(-3))* ( (34*(n-1)^3 + 51*(n-1)^2 + 27*(n-1) +5)*a((n-1)) - (n-1)^3*a((n-1)-1)); fi; end;
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CROSSREFS
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Cf. A059415, A005259.
Sequence in context: A043024 A144889 A098916 this_sequence A108019 A093186 A000765
Adjacent sequences: A059413 A059414 A059415 this_sequence A059417 A059418 A059419
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KEYWORD
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nonn,frac
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jan 30 2001
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