A292617 Convolution of number of partitions into distinct parts and Catalan numbers.

1, 2, 4, 10, 25, 70, 209, 656, 2137, 7155, 24447, 84864, 298374, 1060151, 3800365, 13727145, 49910870, 182522747, 670896855, 2477250003, 9184502747, 34177467134, 127606759053, 477890336663, 1794697782990, 6757164079051, 25501212956975, 96450275088260

Offset: 0

Author

Vaclav Kotesovec, Sep 20 2017

Keywords

• nonn

Crossrefs

Cf. A000009, A000108, A014329.

Programs

Mathematica

Table[Sum[PartitionsQ[k]*CatalanNumber[n-k], {k, 0, n}], {n, 0, 50}]

Formula

a(n) ~ c * 4^n / (sqrt(Pi) * n^(3/2)), where c = QPochhammer[-1, 1/4]/2 = 1.3559096738634793803455442348539593...