A259437 a(n) = Sum_{k=0..n} p(k)^n, where p(k) is the partition function A000041.

1, 2, 6, 37, 724, 20209, 1905630, 191250531, 57659285287, 20931112851787, 17697850924585423, 17720783665888137843, 44421728434157120665320, 117208746422032553556330253, 679595843556865572365153402674, 4907378683411420479410336076467628

Offset: 0

Author

Vaclav Kotesovec, Jun 27 2015

Keywords

• nonn

Crossrefs

Cf. A000041, A133018, A259399, A259436, A259438.

Programs

Mathematica

Table[Sum[PartitionsP[k]^n,{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).