

A131658


For n >= 1, put A_n(z) = Sum_{j>=0} (n*j)!/(j!^n) * z^j and B_n(z) = Sum_{j>=0} (n*j)!/(j!^n) * z^j * (Sum__{k=j+1..j*n} (1/k)), and let u(n) be the largest integer for which exp(B_n(z)/(u(n)*A_n(z))) has integral coefficients. The sequence is u(n).


8



1, 1, 1, 2, 2, 36, 36, 144, 144, 1440, 1440, 17280, 17280, 241920, 3628800, 29030400, 29030400, 1567641600, 1567641600, 156764160000, 49380710400000, 217275125760000, 1086375628800000, 1738201006080000
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OFFSET

1,4


COMMENTS



LINKS



FORMULA

A formula, conditional on a widely believed conjecture, can be found in the article by Krattenthaler and Rivoal (20072009) cited in the references: see Theorem 4 and the accompanying remarks.


CROSSREFS



KEYWORD

nonn


AUTHOR

Christian Krattenthaler (Christian.Krattenthaler(AT)univie.ac.at), Sep 12 2007, Sep 30 2007


STATUS

approved



