A248728 - OEIS

%I #16 Sep 08 2022 08:46:10

%S 1,3,30,3010,18004327,133978259344888,233202632378520643600875145,

%T 817400077628568283525440629036885986580578161120,

%U 37560309092871894517794668078727801667246369744545646936224413217138060330481863103169

%N Number of partitions of 3^n.

%H Alois P. Heinz, <a href="/A248728/b248728.txt">Table of n, a(n) for n = 0..12</a>

%F a(n) = A000041(3^n). - _Michel Marcus_, Oct 18 2014

%F a(n) ~ exp(Pi*sqrt(2*3^(n-1)))/(4*3^(n+1/2)). - _Ilya Gutkovskiy_, Jan 13 2017

%t Table[ PartitionsP[ 3^n], {n, 0, 8}]

%o (Magma) [NumberOfPartitions(3^n): n in [0..8]]; // _Vincenzo Librandi_, Oct 13 2014

%o (PARI) a(n) = numbpart(3^n) \\ _Michel Marcus_, Oct 18 2014

%Y Cf. A000041, A068413, A248730, A248732, A248734, A070177, A248729.

%K nonn

%O 0,2

%A _Robert G. Wilson v_, Oct 12 2014

%E Added a(0)=1 from _Vincenzo Librandi_, Oct 13 2014