

A131657


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_{1<=k<=jn} (1/k)) and let b(n) be the largest integer for which exp(B_n(z)/(b(n)A_n(z))) has integral coefficients. The sequence is b(n).


4



1, 1, 1, 2, 2, 36, 36, 144, 144, 1440, 1440, 17280, 17280, 241920, 3628800, 29030400, 29030400, 1567641600, 1567641600, 783820800000, 9876142080000, 651825377280000, 217275125760000, 8691005030400000
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,4


COMMENTS

Different from A131658 and A056612. The first difference between A056612 and this sequence occurs for n=20, while the first difference between A056612 and A131658 occurs for n=21.


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 Theorem 3 with k=1 in the article by Krattenthaler and Rivoal cited in the references, see the remarks before Theorem 4 in that article.


CROSSREFS

Cf. A007757, A056612, A131658.
Sequence in context: A286375 A056612 A131658 * A298993 A267345 A059523
Adjacent sequences: A131654 A131655 A131656 * A131658 A131659 A131660


KEYWORD

nonn


AUTHOR

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


STATUS

approved



