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
Keywords
Examples
a(10) = 74088 because the partition number of 10 is 42 and 42^3 is 74088.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 0..5000
Programs
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Haskell
a133042 = (^ 3) . a000041 -- Reinhard Zumkeller, Nov 15 2015
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Mathematica
Table[PartitionsP[n]^3, {n, 0, 40}] (* Vaclav Kotesovec, Dec 01 2015 *) -
PARI
for(n=0,20, print1(numbpart(n)^3, ", ")) \\ G. C. Greubel, Oct 02 2017
Formula
a(n) = A000041(n)^3.
a(n) ~ exp(Pi*sqrt(6*n)) / (192*sqrt(3)*n^3). - Vaclav Kotesovec, Dec 01 2015