

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

Different from A131657 and A056612.


LINKS

Christian Krattenthaler, Table of n, a(n) for n = 1..40
Christian Krattenthaler and Tanguy Rivoal, On the integrality of the Taylor coefficients of mirror maps, arXiv:0709.1432 [math.NT], 20072009.
Christian Krattenthaler and Tanguy Rivoal, On the integrality of the Taylor coefficients of mirror maps, II, Communications in Number Theory and Physics, 3(3) (2009), 555591. [Part II appeared before Part I.]
Christian Krattenthaler and Tanguy Rivoal, On the integrality of the Taylor coefficients of mirror maps, Duke Math. J. 151(2) (2010), 175218.


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

Cf. A007757 (bisection at even integers), A056612, A131657.
Sequence in context: A334470 A286375 A056612 * A131657 A298993 A267345
Adjacent sequences: A131655 A131656 A131657 * A131659 A131660 A131661


KEYWORD

nonn


AUTHOR

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


STATUS

approved



