A171485 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 values of B(n).

2, 10, 1168, 624240, 114051456, 353810160000, 9271076400000, 86580328116240000, 19402654331894400000, 15000926812307614080000, 437120128035736887168000, 17196604114594832318160000000

Offset

0,1

Comments

Values of A(n) are given in A171484. P_n(x) are the Legendre Polynomials defined by n!*P_n(x) = (d/dx)^n (x^n*(1-x)^n), see A008316.

Links

Table of n, a(n) for n=0..11.

F. Beukers, A note on the irrationality of zeta(2) and zeta(3), Bull. London Math. Soc., Vol. 11, No. 3 (1979), 268-272.

Wikipedia, Apéry's theorem

Crossrefs

Cf. A002117, A104684.

Sequence in context: A074333 A008559 A245728 * A291882 A215650 A057015

Adjacent sequences: A171482 A171483 A171484 * A171486 A171487 A171488

Keyword

nonn

Author

Max Alekseyev, Dec 09 2009

Status

approved