A171484 Beukers integral int(int( -log(x*y) / (1-x*y) * P_n(2*x-1) * P_n(2*y-1) ,x=0..1,y=0..1)) = (A(n) + B(n)*zeta(3)) / A003418(n)^3. This sequence gives negated values of A(n).

0, 12, 1404, 750372, 137096340, 425299945236, 11144361386340, 104074481089949004, 23323094579273069340, 18031967628526215059268, 525443267415363230379732, 20671296686851400981142679500

Offset: 0

Author

Max Alekseyev, Dec 09 2009

Keywords

• nonn

Comments

Values of B(n) are given in A171485. P_n(x) are the Legendre Polynomials (see A008316) defined by n!*P_n(x) = (d/dx)^n (x^n*(1-x)^n).

Links

• F. Beukers, A note on the irrationality of zeta(2) and zeta(3), Bull. London Math. Soc. 11 (1979) 268-272.
• Wikipedia, Apéry's theorem

Crossrefs

Cf. A104684.