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#15 by Bruno Berselli at Thu Nov 15 11:10:31 EST 2018
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#14 by Michel Marcus at Thu Nov 15 09:27:16 EST 2018
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#13 by Michel Marcus at Thu Nov 15 09:27:12 EST 2018
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A. V. Sills and D. Zeilberger, <a href="https://arxiv.org/abs/1108.4391">Formulae for the number of partitions of n into at most m parts (using the quasi-polynomial ansatz)</a> (>, arXiv:1108.4391 [math.CO])], 2011.
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proposed
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#12 by Jean-François Alcover at Thu Nov 15 09:14:03 EST 2018
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#11 by Jean-François Alcover at Thu Nov 15 09:13:58 EST 2018
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maxExponent = 40; a[0] = 0; a[1] = 1;
a[n_] := Module[{}, aparts = List @@ (Product[1/(1 - x^j), {j, 1, n}] // Apart); cc = aparts + O[x]^maxExponent // CoefficientList[#, x]&; f[k_] = Total[FindSequenceFunction[#, k]& /@ cc]; f[4^n-n(n+1)/2 + 1] // Round];
Table[an = a[n]; Print[n, " ", an]; an, {n, 0, 11}] (* Jean-François Alcover, Nov 15 2018 *)
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approved
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#10 by Alois P. Heinz at Wed Jul 19 15:49:51 EDT 2017
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#9 by Alois P. Heinz at Wed Jul 19 15:49:47 EDT 2017
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A. V. Sills and D. Zeilberger, <a href="httphttps://arxiv.org/abs/1108.4391">Formulae for the number of partitions of n into at most m parts (using the quasi-polynomial ansatz)</a> (arXiv:1108.4391 [math.CO])
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approved
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#8 by Vaclav Kotesovec at Fri Jun 05 17:02:50 EDT 2015
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#7 by Vaclav Kotesovec at Fri Jun 05 17:02:44 EDT 2015
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a(n) ~ 4^(n*(n-1)) / (n!*(n-1)!). - Vaclav Kotesovec, Jun 05 2015
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approved
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#6 by Alois P. Heinz at Tue Mar 11 17:46:31 EDT 2014
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