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%I #5 Dec 01 2015 10:09:10
%S 1,2,3,11,27,270,4366,82491,1762107,135979835,10135979835,
%T 753144350523,130499482241148,20953464347912316,6242774737775732860,
%U 2960555481288609431503,1211886375095917784137679,719537152598665509899534287,851154233276178632011679465423
%N a(n) = Sum_{k=0..n} q(k)^k, where q(k) = partition numbers into distinct parts (A000009).
%F a(n) ~ exp(n^(3/2)*Pi/sqrt(3) + (Pi/(48*sqrt(3)) - 3*sqrt(3)/(8*Pi))*sqrt(n) - 1/32 - 9/(16*Pi^2)) / (3^(n/4) * 4^n * n^(3*n/4)) ~ q(n)^n.
%t Table[Sum[PartitionsQ[k]^k, {k,0,n}], {n,0,20}]
%Y Cf. A259436, A265094.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Dec 01 2015
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