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A259438
a(n) = Sum_{k=0..n} p(k)^(n-k), where p(k) is the partition function A000041.
2
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.
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
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jun 27 2015
STATUS
approved