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

0,3

Links

Table of n, a(n) for n=0..15.

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

Example

a(6)=1771561 because the partition number of 6 is 11 and 11^6=1771561.

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

Mathematica

Table[PartitionsP[n]^n, {n, 0, 15}] (* James C. McMahon, Mar 10 2025 *)

Crossrefs

Cf. A000312, A058694, A062457, A133032, A259373, A265094. Partition numbers: A000041.

Sequence in context: A356806 A120093 A197987 * A210343 A104168 A197990

Adjacent sequences: A133015 A133016 A133017 * A133019 A133020 A133021

Keyword

nonn

Author

Omar E. Pol, Oct 31 2007

Extensions

More terms from R. J. Mathar, Jan 13 2008

a(15) from James C. McMahon, Mar 10 2025

Status

approved