A133018 - OEIS

A133018

Partition number of n, raised to power n.

1, 1, 4, 27, 625, 16807, 1771561, 170859375, 54875873536, 19683000000000, 17080198121677824, 16985107389382393856, 43439888521963583647921, 113809328043328941786781301, 667840509835890864312744140625

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..14.

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

CROSSREFS

Cf. A000312, A058694, A062457, 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

STATUS

approved