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Search: id:A131657
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| A131657 |
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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). |
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+0
4
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| 1, 1, 1, 2, 2, 36, 36, 144, 144, 1440, 1440, 17280, 17280, 241920, 3628800, 29030400, 29030400, 1567641600, 1567641600, 783820800000, 9876142080000, 651825377280000, 217275125760000, 8691005030400000
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OFFSET
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1,4
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COMMENT
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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.
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REFERENCES
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Christian Krattenthaler and Tanguy Rivoal, On the integrality of the Taylor coefficients of mirror maps, preprint, arXiv:0709.1432.
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LINKS
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Christian Krattenthaler, Table of n, a(n) for n = 1..40
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FORMULA
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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.
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CROSSREFS
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Cf. A007757, A056612, A131658.
Sequence in context: A024176 A056612 A131658 this_sequence A059523 A038623 A001121
Adjacent sequences: A131654 A131655 A131656 this_sequence A131658 A131659 A131660
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KEYWORD
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nonn
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AUTHOR
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Christian Krattenthaler (Christian.Krattenthaler(AT)univie.ac.at), Sep 12 2007, Sep 30 2007
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