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

0,2

Links

Table of n, a(n) for n=0..27.

Formula

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

Mathematica

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

Crossrefs

Cf. A000009, A000108, A014329.

Sequence in context: A001998 A005817 A302093 * A148093 A206289 A148094

Adjacent sequences: A292614 A292615 A292616 * A292618 A292619 A292620

Keyword

nonn

Author

Vaclav Kotesovec, Sep 20 2017

Status

approved