%I A059416
%S A059416 1,1,4,36,288,36000,800,1372000,2195200,2667168000,2667168000,28400004864,
%T A059416 3550000608000,311974053431040,7799351335776000,7799351335776000,
%U A059416 1134451103385600,306545704901339904000,6812126775585331200,233621887768698933504000
%N A059416 Denominators of sequence arising from Apery's proof that zeta(3) is irrational.
%D A059416 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.
%H A059416 V. Strehl, <a href="http://www.mat.univie.ac.at/~slc/opapers/s29strehl.html">
               Recurrences and Legendre transform</a>
%F A059416 (n+1)^3*a(n+1) = (34*n^3 + 51*n^2 + 27*n +5)*a(n) - n^3*a(n-1), n >= 
               1.
%e A059416 0, 6, 351/4, 62531/36, ...
%p A059416 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;
%Y A059416 Cf. A059415, A005259.
%Y A059416 Sequence in context: A043024 A144889 A098916 this_sequence A108019 A093186 
               A000765
%Y A059416 Adjacent sequences: A059413 A059414 A059415 this_sequence A059417 A059418 
               A059419
%K A059416 nonn,frac
%O A059416 0,3
%A A059416 N. J. A. Sloane (njas(AT)research.att.com), Jan 30 2001