A133042 - OEIS

%I #11 Oct 03 2017 02:12:33

%S 1,1,8,27,125,343,1331,3375,10648,27000,74088,175616,456533,1030301,

%T 2460375,5451776,12326391,26198073,57066625,117649000,246491883,

%U 496793088,1006012008,1976656375,3906984375,7506509912,14455457856

%N Cubes of partition numbers.

%H Reinhard Zumkeller, <a href="/A133042/b133042.txt">Table of n, a(n) for n = 0..5000</a>

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

%F a(n) ~ exp(Pi*sqrt(6*n)) / (192*sqrt(3)*n^3). - _Vaclav Kotesovec_, Dec 01 2015

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

%t Table[PartitionsP[n]^3, {n, 0, 40}] (* _Vaclav Kotesovec_, Dec 01 2015 *)

%o (Haskell)

%o a133042 = (^ 3) . a000041  -- _Reinhard Zumkeller_, Nov 15 2015

%o (PARI) for(n=0,20, print1(numbpart(n)^3, ", ")) \\ _G. C. Greubel_, Oct 02 2017

%Y Cf. A000578, A030078. Partition number: A000041.

%Y Cf. A001255, A260664.

%K nonn

%O 0,3

%A _Omar E. Pol_, Oct 30 2007