login
A367101
a(n) = Sum_{k=0..n} A000108(k) * A000009(k).
1
1, 2, 4, 14, 42, 168, 696, 2841, 11421, 50317, 218277, 923709, 4043889, 17416089, 76253769, 338014584, 1469460024, 6395962044, 28367342244, 123799554504, 543903261384, 2403339554904, 10545287718864, 46223487538464, 203591793511992, 893988182518176, 3924601439423256
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