A367101 a(n) = Sum_{k=0..n} A000108(k) * A000009(k).

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

Links

Table of n, a(n) for n=0..26.

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

Cf. A000009, A000108, A356270, A367100.

Sequence in context: A228477 A360182 A169982 * A243323 A128750 A047152

Adjacent sequences: A367098 A367099 A367100 * A367102 A367103 A367104

Keyword

nonn

Author

Vaclav Kotesovec, Nov 04 2023

Status

approved