%I A059415
%S A059415 0,6,351,62531,11424695,35441662103,20637706271,963652602684713,
%T A059415 43190915887542721,1502663969043851254939,43786938951280269198311,
%U A059415 13780864457900933987428453,51520703555193710949642777493
%N A059415 Numerators of sequence arising from Apery's proof that zeta(3) is irrational.
%D A059415 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 A059415 V. Strehl, <a href="http://www.mat.univie.ac.at/~slc/opapers/s29strehl.html">
               Recurrences and Legendre transform</a>
%F A059415 (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 A059415 0, 6, 351/4, 62531/36, ...
%p A059415 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 A059415 Cf. A059416, A005259.
%Y A059415 Sequence in context: A144849 A047941 A000409 this_sequence A002684 A036281 
               A064350
%Y A059415 Adjacent sequences: A059412 A059413 A059414 this_sequence A059416 A059417 
               A059418
%K A059415 nonn,frac
%O A059415 0,2
%A A059415 N. J. A. Sloane (njas(AT)research.att.com), Jan 30 2001