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%I #7 Dec 01 2015 10:08:59
%S 1,2,6,33,658,17465,1789026,172648401,55048521937,19738048521937,
%T 17099936170199761,17002207325552593617,43456890729289136241538,
%U 113852784934058230923022839,667954362620824922543667163464,4816707198961510396593071163584840
%N a(n) = Sum_{k=0..n} p(k)^k, where p(k) is the partition function A000041.
%F a(n) ~ p(n)^n ~ exp(1/24 - 3/(4*Pi^2) - (72+Pi^2)*sqrt(n)/(24*sqrt(6)*Pi) + sqrt(2/3)*Pi*n^(3/2)) / (3^(n/2) * 4^n * n^n).
%t Table[Sum[PartitionsP[k]^k,{k,0,n}],{n,0,15}]
%Y Cf. A000041, A133018, A259373, A259399, A259437, A259438, A265095.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Jun 27 2015
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