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A259437
a(n) = Sum_{k=0..n} p(k)^n, where p(k) is the partition function A000041.
2
1, 2, 6, 37, 724, 20209, 1905630, 191250531, 57659285287, 20931112851787, 17697850924585423, 17720783665888137843, 44421728434157120665320, 117208746422032553556330253, 679595843556865572365153402674, 4907378683411420479410336076467628
OFFSET
0,2
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
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jun 27 2015
STATUS
approved