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%I #15 Oct 11 2019 22:41:17
%S 2,10,1168,624240,114051456,353810160000,9271076400000,
%T 86580328116240000,19402654331894400000,15000926812307614080000,
%U 437120128035736887168000,17196604114594832318160000000
%N 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).
%C 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.
%H F. Beukers, <a href="https://doi.org/10.1112/blms/11.3.268">A note on the irrationality of zeta(2) and zeta(3)</a>, Bull. London Math. Soc., Vol. 11, No. 3 (1979), 268-272.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Ap%C3%A9ry%27s_theorem">Apéry's theorem</a>
%Y Cf. A002117, A104684.
%K nonn
%O 0,1
%A _Max Alekseyev_, Dec 09 2009
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