OFFSET
0,2
FORMULA
a(n) ~ 2^(2*n) * exp(Pi*sqrt(n/3)) / (3^(5/4) * sqrt(Pi) * n^(9/4)).
MATHEMATICA
Table[Sum[CatalanNumber[k]*PartitionsQ[k], {k, 0, n}], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Nov 04 2023
STATUS
approved