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%I #4 Jun 27 2015 02:38:26
%S 1,2,6,37,724,20209,1905630,191250531,57659285287,20931112851787,
%T 17697850924585423,17720783665888137843,44421728434157120665320,
%U 117208746422032553556330253,679595843556865572365153402674,4907378683411420479410336076467628
%N a(n) = Sum_{k=0..n} p(k)^n, 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]^n,{k,0,n}],{n,0,15}]
%Y Cf. A000041, A133018, A259399, A259436, A259438.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Jun 27 2015