%I #6 May 27 2015 09:18:50

%S 1,1,1,7,169,7166,436140,34690401,3418486403,402588217564,

%T 55217486292383,8650673262689142,1524827150449505994,

%U 298774748146352115019,64436825369109396329518,15171417879016739747222223,3872658124805520661780283663,1065387724298834666633864592587

%N Number of partitions of n*(n-1)*(n-2) into parts that are at most n.

%H Vaclav Kotesovec, <a href="/A258299/b258299.txt">Table of n, a(n) for n = 0..89</a>

%F a(n) ~ exp(2*n - 11/4) * n^(n-3) / (2*Pi).

%p T:=proc(n,k) option remember; `if`(n=0 or k=1, 1, T(n,k-1) + `if`(n<k, 0, T(n-k,k))) end proc: seq(T(n*(n-1)*(n-2), n), n=0..20);

%Y Cf. A238608, A258297, A258298, A258300, A258301.

%K nonn

%O 0,4

%A _Vaclav Kotesovec_, May 25 2015