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%I #10 Sep 20 2015 09:31:33
%S 0,1,13,43561,455366036161,60209252317216962943201,
%T 291857679749953126623181556402787323521,
%U 120972618144269517756284629487432992029777542693069847287041
%N Number of partitions of (2*n)! into parts that are at most n.
%C Conjecture: If f(n) >= O(n^4) then "number of partitions of f(n) into parts that are at most n" is asymptotic to f(n)^(n-1) / (n!*(n-1)!). For the examples see A238016 and A238010.
%H Vaclav Kotesovec, <a href="/A258670/b258670.txt">Table of n, a(n) for n = 0..21</a>
%H G. J. Rieger, <a href="https://eudml.org/doc/160721">Über Partitionen</a>, Mathematische Annalen (1959), Volume: 138, page 356-362
%H A. V. Sills and D. Zeilberger, <a href="http://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])
%F a(n) ~ (2*n)!^(n-1) / (n!*(n-1)!).
%Y Cf. A236810, A237998, A238000, A238010, A238016, A258668, A258669, A258671.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Jun 07 2015
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