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Search: id:A059415
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| A059415 |
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Numerators of sequence arising from Apery's proof that zeta(3) is irrational. |
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+0
4
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| 0, 6, 351, 62531, 11424695, 35441662103, 20637706271, 963652602684713, 43190915887542721, 1502663969043851254939, 43786938951280269198311, 13780864457900933987428453, 51520703555193710949642777493
(list; graph; listen)
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OFFSET
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0,2
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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. A059416, A005259.
Sequence in context: A144849 A047941 A000409 this_sequence A002684 A036281 A064350
Adjacent sequences: A059412 A059413 A059414 this_sequence A059416 A059417 A059418
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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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