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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). 1
0, 12, 1404, 750372, 137096340, 425299945236, 11144361386340, 104074481089949004, 23323094579273069340, 18031967628526215059268, 525443267415363230379732, 20671296686851400981142679500 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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

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. 11 (1979) 268-272.

Wikipedia, Apery's theorem

CROSSREFS

Cf. A104684.

Sequence in context: A007943 A015512 A004145 * A230519 A235535 A145835

Adjacent sequences:  A171481 A171482 A171483 * A171485 A171486 A171487

KEYWORD

nonn

AUTHOR

Max Alekseyev, Dec 09 2009

STATUS

approved

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Last modified December 5 13:38 EST 2016. Contains 278768 sequences.