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

0,2

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*QPochhammer[1/4, 1/4]) = 1.96926035366826943194719369696726567...

Mathematica

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

Crossrefs

Cf. A000108, A015128, A014329, A292617.

Sequence in context: A190139 A335807 A005580 * A231222 A231436 A027932

Adjacent sequences: A292616 A292617 A292618 * A292620 A292621 A292622

Keyword

nonn

Author

Vaclav Kotesovec, Sep 20 2017

Status

approved