A259436 a(n) = Sum_{k=0..n} p(k)^k, where p(k) is the partition function A000041.

1, 2, 6, 33, 658, 17465, 1789026, 172648401, 55048521937, 19738048521937, 17099936170199761, 17002207325552593617, 43456890729289136241538, 113852784934058230923022839, 667954362620824922543667163464, 4816707198961510396593071163584840

Offset: 0

Author

Vaclav Kotesovec, Jun 27 2015

Keywords

• nonn

Crossrefs

Cf. A000041, A133018, A259373, A259399, A259437, A259438, A265095.

Programs

Mathematica

Table[Sum[PartitionsP[k]^k,{k,0,n}],{n,0,15}]

Formula

a(n) ~ p(n)^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).