A292619 Convolution of number of overpartitions and Catalan numbers.

1, 3, 8, 21, 54, 144, 404, 1195, 3712, 12000, 39994, 136400, 473430, 1665868, 5926476, 21275805, 76964808, 280250088, 1026309908, 3777411342, 13965286180, 51837285776, 193107846304, 721732334136, 2705480787422, 10169387310362, 38320472420462, 144733083435688

Offset: 0

Author

Vaclav Kotesovec, Sep 20 2017

Keywords

• nonn

Crossrefs

Cf. A000108, A015128, A014329, A292617.

Programs

Mathematica

Table[Sum[Sum[PartitionsP[k-j] * PartitionsQ[j], {j, 0, 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*QPochhammer[1/4, 1/4]) = 1.96926035366826943194719369696726567...