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A131658 For n positive, put A_n(z)= sum_j (nj)!/(j!^n) *z^j, B_n(z)= sum_j (nj)!/(j!^n) *z^j * (sum_{j<k<=jn} (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). 4
1, 1, 1, 2, 2, 36, 36, 144, 144, 1440, 1440, 17280, 17280, 241920, 3628800, 29030400, 29030400, 1567641600, 1567641600, 156764160000, 49380710400000, 217275125760000, 1086375628800000, 1738201006080000 (list; graph; refs; listen; history; text; internal format)
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, preprint, arXiv:0709.1432.

FORMULA

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

CROSSREFS

Cf. A007757, A056612, A131657.

Sequence in context: A024176 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

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Last modified July 19 08:23 EDT 2019. Contains 325155 sequences. (Running on oeis4.)