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%I #9 Sep 12 2016 02:41:37
%S 1,1,13,331,13561,776594,57773582,5320252480,586352480958,
%T 75438829494131,11116206652400681,1848033852642973772,
%U 342436117841931383400,70020229273505952925559,15667865938977592230047929,3809417116914053901413289249,1000291703885548521424635046427
%N Number of partitions of n*(n+1)*(n+2) into parts that are at most n.
%H Vaclav Kotesovec, <a href="/A258297/b258297.txt">Table of n, a(n) for n = 0..134</a>
%F a(n) ~ exp(2*n + 13/4) * 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, A258298, A258299, A258300, A258301.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, May 25 2015
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