A259438 a(n) = Sum_{k=0..n} p(k)^(n-k), where p(k) is the partition function A000041.

1, 2, 3, 5, 10, 25, 78, 301, 1414, 7964, 53408, 426116, 4028890, 44697755, 576491980, 8617031811, 149425700853, 3004591733938, 69763130950599, 1860330686377532, 56746090401472922, 1975156902590115291, 78299783319570477185, 3529323014512112469681

Offset: 0

Author

Vaclav Kotesovec, Jun 27 2015

Keywords

• nonn

Comments

The position of the maximum value asymptotically approaches k = n/3.

Crossrefs

Cf. A000041, A133018, A259399, A259436, A259437.

Programs

Mathematica

Table[Sum[PartitionsP[k]^(n-k),{k,0,n}],{n,0,25}]

Formula

log(a(n)) ~ 2^(3/2)*Pi*n^(3/2)/9 - n*log(16*n^2/3)/3.

G.f.: Sum_{k>=0} x^k/(1 - p(k)*x). - Ilya Gutkovskiy, Oct 09 2018