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%I #14 Dec 01 2015 09:38:16
%S 1,1,4,27,625,16807,1771561,170859375,54875873536,19683000000000,
%T 17080198121677824,16985107389382393856,43439888521963583647921,
%U 113809328043328941786781301,667840509835890864312744140625
%N Partition number of n, raised to power n.
%F a(n) = A000041(n)^n.
%F a(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). - _Vaclav Kotesovec_, Jun 23 2015
%e a(6)=1771561 because the partition number of 6 is 11 and 11^6=1771561.
%p A000041 := proc(n) combinat[numbpart](n) ; end: A133018 := proc(n) A000041(n)^n ; end: seq(A133018(n),n=0..18) ; # _R. J. Mathar_, Jan 13 2008
%Y Cf. A000312, A058694, A062457, A259373, A265094. Partition numbers: A000041.
%K nonn
%O 0,3
%A _Omar E. Pol_, Oct 31 2007
%E More terms from _R. J. Mathar_, Jan 13 2008
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