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

0,2

Comments

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

Links

Table of n, a(n) for n=0..23.

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

Mathematica

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

Crossrefs

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

Sequence in context: A107578 A011827 A260304 * A135961 A173253 A011828

Adjacent sequences: A259435 A259436 A259437 * A259439 A259440 A259441

Keyword

nonn

Author

Vaclav Kotesovec, Jun 27 2015

Status

approved