A133018 Partition number of n, raised to power n.
1, 1, 4, 27, 625, 16807, 1771561, 170859375, 54875873536, 19683000000000, 17080198121677824, 16985107389382393856, 43439888521963583647921, 113809328043328941786781301, 667840509835890864312744140625, 4816039244598889571670527496421376
Offset: 0
Keywords
Examples
a(6)=1771561 because the partition number of 6 is 11 and 11^6=1771561.
Programs
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Maple
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
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Mathematica
Table[PartitionsP[n]^n,{n,0,15}] (* James C. McMahon, Mar 10 2025 *)
Formula
a(n) = A000041(n)^n.
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
Extensions
More terms from R. J. Mathar, Jan 13 2008
a(15) from James C. McMahon, Mar 10 2025