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A258298 Number of partitions of n*(n+1)*(n+2)/6 into parts that are at most n.

%I A258298 #6 May 27 2015 09:19:56
%S A258298 1,1,3,14,108,1115,14800,239691,4602893,102442041,2596767156,
%T A258298 73937412122,2338157235782,81358388835166,3090548185022616,
%U A258298 127310130911561966,5654266354725389764,269396637045530725099,13708631585852580662781,742141584297248778501411
%N A258298 Number of partitions of n*(n+1)*(n+2)/6 into parts that are at most n.
%H A258298 Vaclav Kotesovec, <a href="/A258298/b258298.txt">Table of n, a(n) for n = 0..135</a>
%F A258298 a(n) ~ exp(2*n + 9/2) * n^(n-3) / (2*Pi * 6^(n-1)).
%p A258298 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)/6, n), n=0..20);
%Y A258298 Cf. A238608, A258297, A258299, A258300, A258301.
%K A258298 nonn
%O A258298 0,3
%A A258298 _Vaclav Kotesovec_, May 25 2015