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

0,2

Links

Table of n, a(n) for 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).

Mathematica

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

Crossrefs

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

Sequence in context: A241300 A113375 A117266 * A202737 A186648 A372309

Adjacent sequences: A259434 A259435 A259436 * A259438 A259439 A259440

Keyword

nonn

Author

Vaclav Kotesovec, Jun 27 2015

Status

approved