A133042 Cubes of partition numbers.

1, 1, 8, 27, 125, 343, 1331, 3375, 10648, 27000, 74088, 175616, 456533, 1030301, 2460375, 5451776, 12326391, 26198073, 57066625, 117649000, 246491883, 496793088, 1006012008, 1976656375, 3906984375, 7506509912, 14455457856

Offset

0,3

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..5000

Formula

a(n) = A000041(n)^3.

a(n) ~ exp(Pi*sqrt(6*n)) / (192*sqrt(3)*n^3). - Vaclav Kotesovec, Dec 01 2015

Example

a(10) = 74088 because the partition number of 10 is 42 and 42^3 is 74088.

Mathematica

Table[PartitionsP[n]^3, {n, 0, 40}] (* Vaclav Kotesovec, Dec 01 2015 *)

Prog

(Haskell)
a133042 = (^ 3) . a000041  -- Reinhard Zumkeller, Nov 15 2015
(PARI) for(n=0, 20, print1(numbpart(n)^3, ", ")) \\ G. C. Greubel, Oct 02 2017

Crossrefs

Cf. A000578, A030078. Partition number: A000041.

Cf. A001255, A260664.

Sequence in context: A046452 A030078 A051751 * A181361 A056570 A343318

Adjacent sequences: A133039 A133040 A133041 * A133043 A133044 A133045

Keyword

nonn

Author

Omar E. Pol, Oct 30 2007

Status

approved